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chapter, an enhanced virtual synchronous generator control is proposed, ... sharing is achieved based on common ac bus voltage estimation. ...... http://www.vsync.eu/fileadmin/vsync/user/docs/ Workshop3/Karapanos.pdf ...... for their challenging questions which incented me to widen my research from various perspectives.
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Studies on Improving Dynamic Performance of Microgrids by Applying Virtual Synchronous Generator Control to Distributed Generators 劉, 佳

Citation Issue Date Text Version ETD URL

http://hdl.handle.net/11094/55998

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Osaka University

Doctoral Dissertation Studies on Improving Dynamic Performance of Microgrids by Applying Virtual Synchronous Generator Control to Distributed Generators





Jia Liu January 2016

Graduate School of Engineering, Osaka University

Abstract

Abstract Recent years, inverter-interfaced distributed generators (DGs) with renewable energy sources (RES), e.g. photovoltaics and wind turbines, have been developed to solve energy crisis and environmental issues. However, the penetration rate of DGs is limited by current regulations and policies, due to concerns about the increased complexity of power system management and protection, and about the lack of inertia support from these inverter-interfaced DGs. To facilitate the integration of DGs in distribution system, the concept of microgrid was proposed. In a microgrid, a cluster of DGs, distributed energy storage systems and loads operate as a single system to reduce the system complexity for the utility and increase the power quality and reliability for local customers. However, inverter-interfaced DGs with conventional control methods, such as droop control, still cannot provide enough inertia to support the frequency of the microgrid. In this dissertation, virtual synchronous generator (VSG) control, a novel control strategy of DG to provide virtual inertia by emulating the swing equation of a synchronous generator (SG), is introduced to inverter-interfaced DGs in microgrids, in order to improve the dynamic performance, especially the transient response of frequency of microgrids. This dissertation is organized as follows. In Chapter 1, concepts of inverter-interfaced DGs and microgrids, and major challenges in these emerging technologies are introduced. In Chapter 2, principles of the basic VSG control are introduced, and other existing control methods providing virtual inertia support are reviewed. In Chapter 3, VSG control is compared with droop control, which is a conventional DG control method widely adopted in microgrid applications, from the aspect of dynamic characteristics. Two cases are investigated, single inverter operation and parallel operation with a SG. Small-signal models are built to compare transient responses of frequency during a small loading transition, and state-space models are built to analyze oscillation of output active power. Effects of delays in both controls are also studied, and an inertial droop control method is proposed based on the comparison. The results were verified by simulations and experiments. It is shown that VSG control and the proposed inertial droop control inherit the advantages of droop control, and provide extra inertia support for the system. In Chapter 4, parallel operation of multiple VSGs in microgrids is studied. It is shown that when the basic VSG control is applied, active power oscillation and improper transient active power sharing can be observed. Moreover, the problem of reactive power sharing error, inherited from conventional droop control, should also be addressed to obtain desirable steady-state performance. In this chapter, an enhanced virtual synchronous generator control is proposed, with which oscillation -i-

Abstract

damping and proper transient active power sharing are achieved by adjusting the virtual stator reactance based on state-space analyses. Furthermore, communication-less accurate reactive power sharing is achieved based on common ac bus voltage estimation. Simulation and experimental results verified the improvement introduced by the proposed enhanced VSG control strategy. In Chapter 5, a microgrid composed of a VSG and a SG is discussed. Modifications of VSG control are proposed to address specific issues of this kind of microgrids. To prevent unbalanced SG current, double decoupled synchronous reference frame (DDSRF) decomposition and SG negative-sequence current compensation are proposed; and to prevent inverter overcurrent, transient virtual stator impedance is introduced. Tuning methods of main parameters are discussed through theoretical and/or simulation analyses. The effects of the proposed modifications were verified by simulation results, and it is also demonstrated that the presence of VSG alleviates rotor speed deviation of the SG during a loading transition. In Chapter 6, conclusions are presented and some future challenges are discussed.

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Table of Contents

Table of Contents Abstract ..............................................................................................................................................i

Table of Contents ............................................................................................................................ iii

Chapter 1

Introduction ..................................................................................................................1

1.1 Background .............................................................................................................................1 1.2 Inverter-Interfaced Distributed Generators .............................................................................1 1.2.1 Topologies .......................................................................................................................1 1.2.2 Control Methods ..............................................................................................................2 1.2.3 Major Issues .....................................................................................................................4 1.3 Microgrids ...............................................................................................................................5 1.3.1 Main Concept ...................................................................................................................5 1.3.2 Control Schemes ..............................................................................................................6 1.3.3 Major Challenges .............................................................................................................7 1.4 Research Objectives ................................................................................................................8 1.5 Conclusion ............................................................................................................................10 References...................................................................................................................................10

Chapter 2

Principles of Virtual Synchronous Generator Control ...............................................13

2.1 Introduction ...........................................................................................................................13 2.2 Swing Equation of a Synchronous Generator .......................................................................13 2.3 Basic Virtual Synchronous Generator Control Developed by Ise Laboratory ......................14 2.3.1 Control Scheme ..............................................................................................................14 2.3.2 Per Unit Transformation ................................................................................................18 2.3.3 Variations of Virtual Synchronous Generator Control ..................................................19 2.4 Other Existing Inverter Control Methods with Virtual Inertia ..............................................19 2.4.1 VSG Control Developed by VSYNC Project ................................................................20 2.4.2 VISMA Control Developed by IEPE .............................................................................21 2.4.3 VSG Control Developed by KHI ...................................................................................22 2.4.4 Synchronverter ...............................................................................................................24 2.4.5 Other Typical Virtual Inertia Control Methods .............................................................25 2.5 Conclusion ............................................................................................................................26 References...................................................................................................................................26

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Table of Contents

Chapter 3

Dynamic Characteristics Comparisons Between Droop Control and VSG Control ..30

3.1 Introduction ...........................................................................................................................30 3.2 Droop Control .......................................................................................................................31 3.2.1 Overview of Droop Control ...........................................................................................31 3.2.2 Principles of Active Control Part of VSG Control and Droop Control..........................33 3.3 Comparisons of Transient Responses of Frequency .............................................................34 3.3.1 Single Inverter Operation ...............................................................................................34 3.3.2 Parallel Operation with a SG .........................................................................................37 3.3.3 Effects of Delays in Governor Model and P Droop Controller .....................................40 3.3.4 Inertial Droop Control....................................................................................................41 3.4 Comparisons of Active Power Oscillation ............................................................................43 3.5 Simulation Results ................................................................................................................48 3.6 Experimental Results ............................................................................................................50 3.7 Conclusion ............................................................................................................................54 References...................................................................................................................................56

Chapter 4

Parallel Operation of Multiple VSGs in Microgrids ..................................................60

4.1 Introduction ...........................................................................................................................60 4.2 Analyses of Transient Active Power Performance ...............................................................61 4.2.1 Closed-Loop State-Space Model ...................................................................................61 4.2.2 Oscillation Damping ......................................................................................................63 4.2.3 Transient Active Power Sharing ....................................................................................64 4.3 Improvement of Reactive Power Sharing .............................................................................67 4.4 The Proposed Enhanced VSG Control Scheme ....................................................................68 4.5 Simulation Results ................................................................................................................72 4.6 Experimental Results ............................................................................................................75 4.7 Conclusion ............................................................................................................................76 References...................................................................................................................................77

Chapter 5

A VSG Paralleled with a Synchronous Generator in Microgrids ..............................79

5.1 Introduction ...........................................................................................................................79 5.2 System Description ...............................................................................................................80 5.3 The Proposed Modified VSG Control Scheme .....................................................................82 5.4 Discussions on Tuning Methods of Parameters ....................................................................85 5.4.1 Swing Equation Parameters ...........................................................................................85 5.4.2 Governor Delay..............................................................................................................86 5.4.3 Constant Virtual Stator Reactance .................................................................................87 5.4.4 Transient Virtual Stator Impedance for Current Limiting .............................................88 - iv -

Table of Contents

5.5 Simulation Results ................................................................................................................90 5.5.1 Unbalanced Loading Condition .....................................................................................90 5.5.2 Large Loading Transition...............................................................................................92 5.6 Conclusion ............................................................................................................................92 References...................................................................................................................................93

Chapter 6

Conclusions................................................................................................................94

Acknowledgments ..........................................................................................................................96

List of Publications .........................................................................................................................97

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Chapter 1 Introduction

Chapter 1 Introduction 1.1 Background Traditional power system is composed of massive power generation plants, in which the primary energy sources are usually from fossil fuels, hydropower or nuclear power, and a centralized transmission and distribution grid, in which the power flow is usually radical and unidirectional in the distribution level. However, issues of depletion of fossil fuels, geographical and ecological restriction of hydropower and radioactive pollution of nuclear power, have drawn worldwide attentions. Therefore, renewable energy sources (RESs), such as photovoltaics (PVs) and wind turbines, have been considered as the main primary sources of the next generation power system and their penetration ratio in the utility grows year by year. Particularly in Japan, after the Fukushima Daiichi nuclear disaster caused by the Tohoku earthquake and tsunami on 11 March 2011, all nuclear plants have been shut down, which results in a serious shortage of power supply. Therefore, an accelerated growth of RESs is expected in Japan. Although massive wind farms and PV stations have emerged in recent years, most of RESs are usually of small power ratings (less than 10 MW), and are connected directly to the local distribution network. This kind of generators is called distributed generators (DGs) or distributed energy resources (DERs) [1]. DGs are expected to increase the reliability of the power supply by providing backup power generation for local customers. Meanwhile, as DGs are usually located near the loads, if the penetration ratio of DGs increases, it is expected that the transmission loss can be reduced and the transmission/distribution capacity can be relieved [1]. It should be pointed out that besides of RESs, energy source of DGs may come from other clean energy resources, e.g. gas engines and fuel cells, or even traditional diesel engines.

1.2 Inverter-Interfaced Distributed Generators 1.2.1 Topologies Most of DGs are equipped with a power-electronics converter at the output terminal, to convert the generated power to desired voltage and frequency. These converters are usually composed of a dc link and two stages: an input-side converter and a grid-side converter, as depicted in Fig. 1.1 [2]. The input-side converter differs according to energy sources and technologies. For example, for PVs and fuel cells, as PV panels and fuel cells offer a low voltage dc output, usually a boost dc-dc converter is needed; whereas for wind turbines and gas engines, an ac-dc rectifier is required. The con-

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Chapter 1 Introduction

Fig. 1.1

General structure of inverter-interfaced distributed generators.

trol strategy of input-side converter is responsible for the regulation of dc-link or energy source, e.g. maintaining dc-link voltage or tracking the maximum power point. On the other hand, the grid-side converter is always a dc-ac inverter, no matter what energy source. The control strategy of the grid-side converter is responsible for regulation of generated power, output voltage and frequency and other power quality issues, and is less dependent on the energy source [2]. As a result, this type of DGs can be classified into the same category, called inverter-interfaced DGs. In most cases, an energy storage system is connected to the dc link, especially for non-dispatchable inverter-interfaced DGs such as wind turbines and photovoltaics, to provide an energy buffer for balancing the active power converted in two stages. The dc-link storage may be an electrolytic capacitor, an electric double-layer capacitor (EDLC) or a battery. A dc-dc converter may be needed for EDLCs and batteries, for conversion of voltage level, regulation of dc-link voltage and/or management of state of charge (SOC). It should be mentioned that not all DGs are inverter-interfaced DGs. Some DGs can be connected directly or partially directly to the grid. Moreover, some power-electronics-interfaced DGs may only consist of a single stage. These exceptions are not discussed in this dissertation. Furthermore, this dissertation focuses on the control strategy of grid-side converter. In most cases, energy source, input-side converter and energy storage are omitted, and the dc-link is considered as an infinite dc source.

1.2.2 Control Methods Generally, conventional control methods of the grid-side converter can be classified into two basic types: grid-forming control and grid-feeding control [3]. Grid-forming control is also known as voltage source control or VF control, because it fixes the voltage and frequency at the output terminal to create a voltage source, as shown in Fig. 1.2(a). An -2-

Chapter 1 Introduction

Fig. 1.2

Control methods of grid-side converter. (a) Grid-forming control. (b) Grid-feeding control.

(c) Voltage-source-based grid-supporting control. (d) Current-source-based grid-supporting control. [4]

inverter-interfaced DG equipped with this control method is able to form an individual islanded network, but is not suitable for parallel operation with other voltage sources, e.g. with the main grid or with another DG equipped with grid-forming control. Grid-feeding control is also known as current source control or PQ control, because it controls the output active and reactive power by control the amplitude and phase angle of the current injected into the ac bus, as illustrated in Fig. 1.2(b). Grid-feeding control cannot work individually because it requires a voltage source to provide voltage supporting and phase angle reference. Commonly a phase-locked loop (PLL) is used in this control to synchronize the inverter to the grid. The output active power may be a fixed value for a dispatchable DG, or a variant value determined by maximum power point tracking algorithm of the input-side converter. The output reactive power may be 0 for DGs of unity power factor, and other dispatched value to compensate a known reactive power flow in nearby area. However, in some applications, e.g. in a microgrid configuration discussed in Section 1.3, multiple DGs are required to operate in both islanded mode and grid-connected mode. Obviously, conventional grid-forming control and grid-feeding control are not competent in this context. Therefore, grid-supporting control is developed to address this issue [3]. In grid-supporting control, usually control laws between frequency and active power, and between voltage and reactive power are predefined in the control strategies, in order to automatically share the active and reactive power between parallel generators. These control laws have been developed in conventional synchronous generator (SG) control, and are adopted for inverters known as droop control [5], [6], because these control laws are generally linear relations with a negative slope.

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Chapter 1 Introduction

Grid-supporting control can be further classified into voltage-source-based and current-sourcebased grid-supporting control. Current-source-based grid-supporting control can be considered as an upgraded grid-feeding control, as its inner control loop is in fact a grid-feeding control, with the added droop control laws only providing automatic power sharing ability, as shown in Fig. 1.2(d). Therefore, like grid-feeding control, DGs with current-source-based grid-supporting control still need to be connected to a voltage source as it cannot provide voltage support for the system. On the other hand, voltage-source-based grid-supporting control is developed from grid-forming control, as illustrated in Fig. 1.2(c). Therefore, DGs with voltage-source-based grid-supporting control can operate individually owing to the voltage source feature. Moreover, with the added droop control laws, it can even operate in parallel with other voltage sources, no matter whether it is another DG with voltage-source-based grid-supporting control or a fixed voltage source, e.g. the main grid. That is to say, droop control laws provide not only automatic power sharing ability, but also parallel operation ability for a voltage-source-based inverter. Owing to its versatile applicability, voltage-source-based grid-supporting control is arguably the most promising control type for the grid-side converter of inverter-interfaced DGs.

1.2.3 Major Issues Although the development of DGs is a promising direction of the future “smart grid”, the increased penetration of DGs is in fact not friendly to the traditional power system. Major issues caused by inverter-interfaced DGs include the following [1]: (1)

Unintentional islanding. Unintentional islanding refers to the situation in which a DG continues to provide power supply for its nearby area unintentionally during a period in which the main grid is not available. It may be dangerous for the utility operators, who may not be aware that the devices are still powered. Moreover, some temporary grid faults can be solved by auto reclosing of relays, and it may become less effective if an unintentional islanding happens. As a result, in current power system regulations, e.g. IEEE Standard 1547 [7], DGs must detect unintentional islanding events and disconnect themselves from the grid. That is to say, DGs cannot be counted as backup power supply during a grid fault under an unintentional islanding.

(2)

Increased complexity of relay protection. Traditional relay protection in distribution system is designed for a radical configuration. However, the connection of DGs complicates the power flow and makes it bidirectional and unpredictable.

(3)

Lack of inertia. Traditional power system is supplied mainly by synchronous generators (SGs), which normally have a kinetic energy reservoir in rotating mass. During transient power shortage, this inertia can temporarily provide additional power supply with a fast response, thus maintain the transient frequency. However, inverter-interfaced DGs have very poor inertia. If traditional SGs are gradually replaced by inverter-interfaced DGs, the total inertia of the system will certainly decrease. -4-

Chapter 1 Introduction

A radical solution for the first two issues can be achieved by integrated management of the nearby area of DGs, which is known as the concept of “microgrid” discussed in next section. As for the third one, a promising solution is to apply inverter control methods with virtual inertia, which are presented in detail in Chapter 2.

1.3 Microgrids 1.3.1 Main Concept The concept of microgrid is originally proposed by Prof. R. H. Lasseter in [8]. In a microgrid, a cluster of DGs, distributed energy storage systems (DESSs) and loads are managed to operate as a single system, as it is illustrated in Fig. 1.3. It is connected to the main grid through a single point, which is called the point of common coupling (PCC), thus it can be considered as a single dispatched load or source by the grid supervisor. Therefore, the system complexity for the utility can be significantly reduced. Loads in a microgrid can be connected to either a dc bus or an ac bus, and can be shed according to a predefined priority in order to guarantee the power supply for sensitive loads. A microgrid usually has two operation modes: grid-connected mode and islanded mode. During grid-connected mode, the microgrid consumes or supplies a dispatched amount of power through the PCC. If a grid fault happens or the power quality of the grid falls below a predefined level, the microgrid can be switched automatically and seamlessly to islanded mode, i.e., using internal DGs and DESSs to maintain the power supply to internal loads. It should be pointed out that the islanded mode of a microgrid is different from the aforementioned unintentional islanding. It is an intentional islanding which is predictable and under control. Therefore, the power quality and reliability of power supply for local customers can be increased by adopting a microgrid configuration.

Fig. 1.3

An example of a microgrid configuration.

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Chapter 1 Introduction

1.3.2 Control Schemes The control strategy of a microgrid can be classified into three categories: master-slave control, peer-to-peer control and hierarchical control. (1)

In master-slave control, one DC/AC inverter is chosen as master unit and other inverters are considered as slave units. Grid-feeding control is usually adopted for both master unit and slave units in grid-connected mode. However, in islanded mode, the master unit should be changed into grid-forming control to provide a voltage source for slave units, which are still controlled by grid-feeding control [9]. As a transfer of control method of master unit is inevitable, the transient performances of master-slave control during connection and disconnection are relatively poor. Furthermore, the reliability of master-slave control is also a problem, because the microgrid cannot operate in islanded mode if the master unit is out of service. Another restriction degrading the reliability of microgrid is that communication between the master unit and the main breaker of the microgrid is required.

(2)

Peer-to-peer control can be classified into two categories, i.e. with or without communication between inverters. The former is typically based on a multi-agent control scheme [10], [11], and the latter is achieved by applying voltage-source-based grid-supporting control to the inverters [12], [13]. In the peer-to-peer control based on voltage-source-based grid-supporting control, no communication between inverters is required, and no change of inverter control method is needed during microgrid mode transition, because the active and reactive power can be shared coordinately based on the synchronized frequency and local voltage measurement according to the predefined droop control laws. Therefore, communication-less peer-to-peer control is widely adopted in recent microgrid applications.

(3)

Hierarchical control is developed from the peer-to-peer control [14], [15]. The primary control level of a hierarchical microgrid control is normally the aforementioned peer-to-peer control installed in inverters, which is responsible for the basic operation of the microgrid. The secondary control and sometimes a tertiary control are installed in a microgrid central controller (MGCC), which usually situates near the main breaker of the microgrid. The secondary control and tertiary control are responsible for optimized operation of the microgrid, e.g., restoring the frequency and voltage deviation, adjusting reactive power sharing error, optimizing power management and controlling power flow at the PCC in grid-connected mode. Communication between MGCC and inverters are required to apply the secondary and tertiary control. However, even during a communication failure, the primary control is still available to maintain the basic operation of the microgrid. In this situation, hierarchical control is downgraded to the aforementioned peer-to-peer control.

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Chapter 1 Introduction

1.3.3 Major Challenges With voltage-source-based grid-supporting control installed in the inverters, the basic operation of a microgrid can be established. However, there are still some challenges to be addressed, in order to achieve better overall performance. (1)

Proper steady-state active and reactive power sharing. Generally, active and reactive power is expected to be shared according to the generator power rating ratio in a microgrid. If the microgrid is based on 𝑃 − 𝜔 and 𝑄 − 𝑉 droop control scheme, the active power can be shared correctly because frequency is auto-synchronized at the output terminal of all inverters in the steady state. However, output voltage may differ due to line voltage drops, which results in inaccurate reactive power sharing. If the microgrid is based on 𝑃 − 𝑉 and 𝑄 − 𝜔 droop control scheme, the inaccurate power sharing will be observed in active power. In previous studies, this issue is address by improved control schemes at the primary control level [16]–[23], or by adding correction algorithms at secondary control level [24]–[29]. This issue is further discussed in Chapter 4, and a new approach is proposed.

(2)

Transient power sharing. Even if steady-state power is correctly shared as desired, transient power may not be shared properly due to different dynamic performance of DGs in a microgrid. If this issue is not properly addressed, transient overcurrent may stop inverters. This issue usually occurs during parallel operation of a SG and an inverter-interfaced DG [4], [30], and even during parallel operation of inverters. This issue is discussed in Chapter 4 for the case of parallel inverters, and in Chapter 5 for the case of parallel operation of a SG and an inverter-interfaced DG.

(3)

Frequency and voltage restoration. As frequency and voltage are drooped against active and reactive power in voltage-source-based grid-supporting control, the deviated frequency and voltage deteriorate power quality of a microgrid. A general approach to address this issue is restoring frequency and voltage by changing the set value of active and reactive power in droop control laws at the secondary control level [13]–[15].

(4)

Optimized power management. The optimized active and reactive power sharing is not always based on generator power rating ratio. Economic and environmental concerns like fuel consumption and CO2 emission may require a different power sharing among the DGs. This rearrangement of power sharing can be achieved by changing the set value of active and reactive power in droop control law at the secondary control level [31], [32]. As for reactive power management, a method to fully utilize the power ratings of DGs for reactive power supporting is proposed in [33].

(5)

Unbalanced and nonlinear Load. When unbalanced and nonlinear loads are connected to a microgrid, proper sharing of negative-sequence and harmonic current becomes important. Additional controllers dedicated to negative-sequence and harmonic current sharing are required, as it is proposed in [34], [35]. Moreover, if a SG is installed in a microgrid, as nega-7-

Chapter 1 Introduction

tive-sequence and harmonic current will heat the SG, proper control method should be applied in order to prevent negative-sequence and harmonic current in the SG, as it is discussed in Chapter 5. (6)

Seamless transfer between islanded mode and grid-connected mode. As mentioned previously, when a grid fault or a deterioration of grid power quality is detected, microgrids should transfer to islanded mode. When high power quality grid power supply is available again, microgrid can be reconnected to the grid through a synchronizing process. The transfer between grid-connected mode and islanded mode should be seamless, i.e. the amplitude, phase, and frequency of bus voltage should be kept stable. This seamless transfer is generally achieved by the secondary or tertiary control in the MGCC, and the synchronizing process is achieved by changing the set value of active and reactive power in droop control laws [14]. An alternative method with less communication requirement is proposed in [36].

(7)

Power flow control in grid-connected mode. The power flow at the PCC can be controlled to a constant value in grid-connected mode, in order to operate in a grid-friendly manner. This function can be realized at the secondary or tertiary level in the MGCC [14].

(8)

Inertia support. Conventional voltage-source-based grid-supporting control methods, e.g. droop-control-based methods only emulate the steady-state output characteristics of a SG. The kinetic energy reservoir in the rotating mass of a SG is not emulated in the conventional droop control method. As a result, like most of other inverter control methods, droop control cannot provide enough inertia support. Therefore, a droop-control-based microgrid usually has very poor inertia. After a large disturbance, e.g. connection of a large load or a ground fault, the frequency of microgrid may deviate too fast to be kept within the tolerance by frequency restoration control. Modified droop control method is proposed to address this problem [37]; however, more radical solutions are still expected. Therefore, in this dissertation, a novel voltage-source-based grid-supporting control method, called virtual synchronous generator (VSG) control, mimicking not only the steady-state characteristics of SGs, but also their transient characteristics by applying swing equation, is applied to inverter-interfaced DG, in order to provide inertia support for the microgrid.

1.4 Research Objectives As it is discussed in the previous parts of this chapter, microgrid is a promising configuration for the integration of DGs into the power system, and voltage-source-based grid-supporting control is currently the most adopted control method for inverter-interfaced DGs in a microgrid. However, conventional voltage-source-based grid-supporting control, e.g. conventional droop control, cannot provide enough inertia support. In this dissertation, the VSG concept is applied to the inverter-interfaced DGs, as shown in Fig. 1.4, in order to enhance the inertia of microgrids and to improve the dynamic performance, especially the transient response of frequency of microgrids. First, it is shown with an analytical approach that VSG control can provide better dynamic performance than -8-

Chapter 1 Introduction

Fig. 1.4

Fig. 1.5

Applying VSG control in a microgrid.

Main themes of Chapter 4 and Chapter 5.

conventional droop control. Afterwards, the operation methods of parallel VSGs and parallel operation of a VSG and a SG are established. Other issues of microgrids, e.g., proper steady-state reactive power sharing, transient power sharing, and unbalanced loading condition are also addressed in this dissertation. Detailed discussions in following chapters are organized as follows. In Chapter 2, principles of basic VSG control are introduced. In Chapter 3, the dynamic characteristics of VSG are compared with those of droop control, to clarify the advantage and disadvantage of VSG control over conventional inertia-less voltage-source-based grid-supporting control. In Chapter 4 and Chapter 5, parallel -9-

Chapter 1 Introduction

operation of multiple VSGs, and parallel operation of a VSG and a SG are studied, respectively, as it is shown in Fig. 1.5. Special issues introduced by VSG control, such as active power oscillation and transient active power sharing, and other well-known challenges of microgrids, e.g. steady-state reactive power sharing and unbalanced loading condition, are also addressed. With the analyses and the proposed VSG control schemes presented in this dissertation, the basic operation of inertial microgrids based on VSG control can be established.

1.5 Conclusion In this chapter, the background of this dissertation was introduced. Main concepts, such as inverter-interfaced DG and microgrid were explicated. The control methods equipped in inverter-interfaced DGs and the overall control schemes of microgrids were discussed. Major issues and challenges of inverter-interfaced DGs and microgrids were discussed. Finally, the main research objectives of this dissertation were presented.

References [1]

R. C. Dugan and T. E. McDermott, “Distributed generation,” IEEE Ind. Appl. Mag., vol. 8, no. 2, pp. 19–25, Mar./Apr. 2002.

[2]

F. Blaabjerg, R. Teodorescu, M. Liserre, and A. V. Timbus, “Overview of control and grid synchronization for distributed power generation systems,” IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1398–1409, Oct. 2006.

[3]

J. Rocabert, A. Luna, F. Blaabjerg, and P. Rodríguez, “Control of power converters in AC microgrids,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4734–4749, Nov. 2012.

[4]

A. D. Paquette and D. M. Divan, “Virtual impedance current limiting for inverters in microgrids with synchronous generators,” IEEE Trans. Ind. Appl., vol. 51, no. 2, pp. 1630– 1638, Mar./Apr. 2015.

[5]

M. C. Chandorkar, D. M. Divan, and R. Adapa, “Control of parallel connected inverters in standalone ac supply systems,” IEEE Trans. Ind. Appl., vol. 29, no. 1, pp. 136–143, Jan./Feb. 1993.

[6]

K. Debrabandere, B. Bolsens, J. Van den Keybus, A.Woyte, J. Driesen, and R. Belmans, “A voltage and frequency droop control method for parallel inverters,” IEEE Trans. Power Electron., vol. 22, no. 4, pp. 1107–1115, Jul. 2007.

[7]

IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems, IEEE Standard 1547-2003, Jul. 2003.

[8]

R. H. Lasseter, “MicroGrids,” in Proc. 2002 IEEE Power Eng. Soc. Winter Meeting, pp. 305– 308.

[9]

B. Zhao, X. Zhang, and J. Chen, “Integrated Microgrid Laboratory System,” IEEE Trans. Power Syst., vol. 27, no. 4, pp. 2175–2185, Nov. 2012.

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Chapter 1 Introduction [10] M. E. Baran and I. M. El-Markabi, “A multiagent-based dispatching scheme for distributed generators for voltage support on distribution feeders,” IEEE Trans. Power Syst., vol. 22, no. 1, pp. 52–59, Feb. 2007. [11] A. L. Dimeas and N. D. Hatziargyriou, “Operation of a multiagent system for microgrid control,” IEEE Trans. Power Syst., vol. 20, no. 3, pp. 1447–1455, Aug. 2005. [12] H. Nikkhajoei and R. H. Lasseter, “Distributed generation interface to the CERTS microgrid,” IEEE Trans. Power Del., vol. 24, no. 3, pp. 1598–1608, Jul. 2009. [13] F. Katiraei and M. R. Iravani, “Power management strategies for a microgrid with multiple distributed generation units,” IEEE Trans. Power Syst., vol. 21, no. 4, pp. 1821–1831, Nov. 2006. [14] J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. De Vicuña, and M. Castilla, “Hierarchical control of droop-controlled DC and AC microgrids—A general approach towards standardization,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 158–172, Jan. 2011. [15] A. Bidram and A. Davoudi, “Hierarchical structure of microgrids control system,” IEEE Trans. Smart Grid, vol. 3, no. 4, pp. 1963–1976, Dec. 2012. [16] J. He, Y. W. Li, J. M. Guerrero, F. Blaabjerg, and J. C. Vasquez, “An islanding microgrid power sharing approach using enhanced virtual impedance control scheme,” IEEE Trans. Power Electron., vol. 28, no. 11, pp. 5272–5282, Nov. 2013. [17] Y. Zhu, Z. Fang, F. Wang, B. Liu, and Y. Zhao, “A wireless load sharing strategy for islanded microgrid based on feeder current sensing,” IEEE Trans. Power Electron., vol. 30, no. 12, pp.6706–6719, Dec. 2015. [18] Y. W. Li and C.-N. Kao, “An accurate power control strategy for power-electronics-interfaced distributed generation units operating in a low-voltage multibus microgrid,” IEEE Trans. Power Electron., vol. 24, no. 12, pp. 2977–2988, Dec. 2009. [19] Q.-C. Zhong, “Robust droop controller for accurate proportional load sharing among inverters operated in parallel,” IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1281–1290, Apr. 2013. [20] C. K. Sao and P. W. Lehn, “Autonomous load sharing of voltage source converters,” IEEE Trans. Power Del., vol. 20, no. 2, pp. 1009–1016, Apr. 2005. [21] C-.T. Lee, C-.C. Chu, and P-.T. Cheng, “A new droop control method for the autonomous operation of distributed energy resource interface converters,” IEEE Trans. Power Electron., vol. 28, no. 4, pp. 1980–1993, Apr. 2013. [22] E. Rokrok and M. E. H. Golshan, “Adaptive voltage droop scheme for voltage source converters in an islanded multibus microgrid,” IET Gener. Transm. Distrib., vol. 4, no. 5, pp. 562–578, May 2010. [23] H. Xu, X. Zhang, F. Liu, R. Shi, C. Yu, W. Zhao, Y. Yu, and W. Cao, “A reactive power sharing method based on virtual capacitor in islanding microgrid,” in Proc. Int. Power Electron. Conf. (IPEC-Hiroshima ECCE-Asia), 2014, pp. 567–572.

- 11 -

Chapter 1 Introduction [24] J. He and Y. W. Li, “An enhanced microgrid load demand sharing strategy,” IEEE Trans. Power Electron., vol. 27, no. 9, pp. 3984–3995, Sept. 2012. [25] J. He, Y. W. Li, and F. Blaabjerg, “An enhanced islanding microgrid reactive power, imbalance power, and harmonic power sharing scheme,” IEEE Trans. Power Electron., vol. 30, no. 6, pp. 3389–3401, Jun. 2015. [26] H. Mahmood, D. Michaelson, and J. Jiang, “Accurate reactive power sharing in an islanded microgrid using adaptive virtual impedances,” IEEE Trans. Power Electron., vol. 30, no. 3, pp. 1605–1617, Mar. 2015. [27] H. Han, Y. Liu, Y. Sun, M. Su, and J. M. Guerrero, “An improved droop control strategy for reactive power sharing in islanded microgrid,” IEEE Trans. Power Electron., vol. 30, no. 6, pp. 3133–3141, Jun. 2015. [28] Q. Shafiee, J. M. Guerrero, and J. C. Vasquez, “Distributed secondary control for islanded microgrids — a novel approach,” IEEE Trans. Power Electron., vol. 29, no. 2, pp. 1018–1031, Feb. 2014. [29] A. Micallef, M. Apap, C. Spiteri-Staines, J. M. Guerrero, and J. C. Vasquez, “Reactive power sharing and voltage harmonic distortion compensation of droop controlled single phase islanded microgrids,” IEEE Trans. Smart Grid, vol. 5, no. 3, pp. 1149–1158, May 2014. [30] A. D. Paquette, M. J. Reno, R. G Harley, and D. M. Divan, “Sharing transient loads: causes of unequal transient load sharing in islanded microgrid operation,” IEEE Ind. Appl. Mag., vol. 20, no. 2, pp. 23–34, Mar./Apr. 2014. [31] C. A Hernandez-Aramburo, T. C. Green, and N. Mugniot, “Fuel consumption minimization of a microgrid,” IEEE Trans. Ind. Appl., vol. 41, no. 3, pp. 673–681, May/Jun. 2005. [32] E. Barklund, N. Pogaku, M. Prodanovic, C. Hernandez-Aramburo, and T.C. Green, “Energy management in autonomous microgrid using stability-constrained droop control of inverters,” IEEE Trans. Power Electron., vol. 23, no. 5, pp. 2346–2352, Sept. 2008. [33] A. Milczarek, M. Malinowski, and J. M. Guerrero, “Reactive power management in islanded microgrid—proportional power sharing in hierarchical droop control,” IEEE Trans. Smart Grid, vol. 6, no. 4, pp. 1631–1638, Jul. 2015. [34] M. B. Delghavi and A. Yazdani, “Islanded-mode control of electronically coupled distributed-resource units under unbalanced and nonlinear load conditions,” IEEE Trans. Power Del., vol. 26, no. 2, pp. 661–673, Apr. 2011. [35] Q.-C. Zhong, “Harmonic droop controller to reduce the voltage harmonics of inverters,” IEEE Trans. Ind. Electron., vol. 60, no. 3, pp. 936–945, Mar.2013. [36] Y. Jia, D. Liu, and J. Liu, “A novel seamless transfer method for a microgrid based on droop characteristic adjustment,” in Proc. 7th Int. Power Electron. and Motion Control Conf., 2012, pp. 362–367. [37] N. Soni, S. Doolla, and M. C. Chandorkar, “Improvement of transient response in microgrids using virtual inertia,” IEEE Trans. Power Del., vol. 28, no. 3, pp. 1830–1838, Jul. 2013. - 12 -

Chapter 2 Principles of Virtual Synchronous Generator Control

Chapter 2 Principles of Virtual Synchronous Generator Control 2.1 Introduction In this chapter, principles of VSG control schemes are introduced, beginning with the swing equation of a real SG shown in Section 2.2. The basic VSG control scheme proposed by Ise Laboratory, Osaka University, from which the control methods in this dissertation are developed, is discussed in detail in Section 2.3. A brief survey of other existing inverter-interfaced DG control methods with virtual inertia support is presented in Section 2.4.

2.2 Swing Equation of a Synchronous Generator Fig. 2.1 illustrates the dynamic model of a synchronous generator connected to an infinite bus. The input power 𝑃𝑖𝑛 is provided by the shaft torque 𝑇𝑚 as shown in (2.1). 𝑃𝑖𝑛 = 𝑇𝑚 𝜔𝑚 ,

(2.1)

where 𝜔𝑚 is the angular frequency of the rotor. In this dissertation, it is assumed that the number of pairs of poles is 1. The relation between output power 𝑃𝑜𝑢𝑡 and the input power 𝑃𝑖𝑛 is written as 𝑃𝑖𝑛 − 𝑃𝑜𝑢𝑡 = 𝐽𝜔𝑚

d𝜔𝑚 + 𝐷(𝜔𝑚 − 𝜔𝑔 ), d𝑡

(2.2)

where 𝜔𝑔 is the angular frequency of the bus, 𝐽 is the moment of inertia of rotating mass, and 𝐷 is the damping factor of the damping power introduced by the damp winding, which depends on the power angle 𝛿 and SG impedance parameters as shown in (2.3) [1]. 2 𝐷 = 𝑉𝑏𝑢𝑠 [

𝑇′′𝑞 𝑋′𝑞 (𝑋′𝑞 − 𝑋′′𝑞 ) 𝑇′′𝑑 𝑋′𝑑 (𝑋′𝑑 − 𝑋′′𝑑 ) 2 2 sin 𝛿 + 2 cos 𝛿], 𝑋′′𝑑 (𝑋′𝑑 + 𝑋𝑙𝑖𝑛𝑒 )2 𝑋′′ (𝑋′ + 𝑋 ) 𝑞

Fig. 2.1

𝑞

𝑙𝑖𝑛𝑒

Dynamic model of synchronous generator.

- 13 -

(2.3)

Chapter 2 Principles of Virtual Synchronous Generator Control where 𝑉𝑏𝑢𝑠 is the amplitude of bus voltage, 𝑋𝑙𝑖𝑛𝑒 is the line reactance, 𝑋′𝑑 , 𝑋′′𝑑 , 𝑋′𝑞 , 𝑋′′𝑞 are the d-axis and q-axis transient and sub-transient reactance of the SG, respectively, 𝑇′′𝑑 and 𝑇′′𝑞 are the d-axis and q-axis sub-transient short-circuit time constant of the SG, respectively. Knowing that (2.3) is only valid if mechanical losses are neglected and the rotor flux linkage is fixed. The latter is not true if automatic voltage regulator (AVR) is applied. However, (2.3) can be still used to obtain an approximate value. Equation (2.2) is known as swing equation, which describes the inertia feature of a traditional SG. The kinetic energy 𝑊 stored in the rotating mass can be deduced as 1 2 𝑊 = 𝐽𝜔𝑚 . 2

(2.4)

This kinetic energy reservoir is essential for the transient power balance between 𝑃𝑖𝑛 and 𝑃𝑜𝑢𝑡 . According to the swing equation shown in (2.2), if 𝑃𝑖𝑛 > 𝑃𝑜𝑢𝑡 , 𝜔𝑚 increases, and 𝑊 increases, the surplus generated power is stored in the rotating mass. If 𝑃𝑖𝑛 < 𝑃𝑜𝑢𝑡 , 𝜔𝑚 decreases, and 𝑊 decreases, the stored kinetic energy is fed into the power system to compensate transient power shortage. In steady state, 𝜔𝑚 = 𝜔𝑔 and d𝜔𝑚 /d𝑡 = 0; therefore, 𝑃𝑖𝑛 = 𝑃𝑜𝑢𝑡 .

2.3 Basic Virtual Synchronous Generator Control Developed by Ise Laboratory 2.3.1 Control Scheme Fig. 2.2 shows the basic virtual synchronous generator (VSG) control scheme, developed through [2], [3] by the research team in Ise Laboratory, Osaka University. The key idea of the VSG control is to emulate the swing equation in the block “Swing Equation Function” in Fig. 2.2. For simplification, the damping factor 𝐷 is considered as a constant parameter. This simplification does not affect the basic principle of the swing equation. As an inverter does

Fig. 2.2

Block diagram of the basic VSG control scheme.

- 14 -

Chapter 2 Principles of Virtual Synchronous Generator Control

Fig. 2.3

Fig. 2.4

Flow chart of solving swing equation by Runge-Kutta method.

Block diagram of the “Frequency Detector” block of the basic VSG control.

not really have a rotating mass, the moment of inertia 𝐽 and the damping factor 𝐷 are in fact virtual parameters defined in the inverter control program. As the swing equation (2.2) is a differential equation, an algorithm based on Runge-Kutta iterative method is adopted to solve the virtual rotor angular frequency 𝜔𝑚 from (2.2), as shown in Fig. 2.3. The calculated 𝜔𝑚 provides the frequency reference for the governor model and the PWM inverter phase reference 𝜃𝑝𝑤𝑚 through an integrator. The kinetic energy stored in the rotating mass expressed in (2.4) is emulated by the energy storage, which performs as an energy buffer between the input power generated by the DG and the output power distributed to the ac bus. Normally the energy storage is a capacitor. An electric dou-

- 15 -

Chapter 2 Principles of Virtual Synchronous Generator Control

ble-layer capacitor (EDLC) or a battery can be optionally used combined with the capacitor if large capacity is required. The block “Frequency Detector” is responsible for the detection of bus frequency 𝜔𝑔 . In this dissertation, a conventional phase-locked loop (PLL) is used to trace the frequency of output voltage 𝑽𝑜𝑢𝑡 , as shown in Fig. 2.4. The transformation from three-phase components to αβ-frame components is executed through the pre-multiplication by the transformation matrix 𝑻𝑎𝑏𝑐/𝛼𝛽 defined as follows. 2

𝑻𝑎𝑏𝑐/𝛼𝛽 = √ ∙ 3

1

[0



1 2

√3 2

− −

1 2

√3

(2.5)

2]

It should be pointed out that in transient state, the frequency of output voltage may differ from the bus frequency, especially if the line impedance 𝑍𝑙𝑖𝑛𝑒 is very large. However, measurement of bus voltage is usually difficult as the inverter may be installed far away from the ac bus of the microgrid. Normally, the influence of this compromise can be neglected as the line impedance 𝑍𝑙𝑖𝑛𝑒 in a microgrid is usually small. In the block “Power Meter”, the output active and reactive power 𝑃𝑜𝑢𝑡 and 𝑄𝑜𝑢𝑡 are calculated through (2.6) and (2.7). 𝑃𝑜𝑢𝑡 = 𝑣𝑜𝑢𝑡_𝑎 𝑖𝑜𝑢𝑡_𝑎 + 𝑣𝑜𝑢𝑡_𝑏 𝑖𝑜𝑢𝑡_𝑏 + 𝑣𝑜𝑢𝑡_𝑐 𝑖𝑜𝑢𝑡_𝑐

𝑄𝑜𝑢𝑡 =

1 √3

[𝑖𝑜𝑢𝑡_𝑎 (𝑣𝑜𝑢𝑡_𝑏 − 𝑣𝑜𝑢𝑡_𝑐 ) + 𝑖𝑜𝑢𝑡_𝑏 (𝑣𝑜𝑢𝑡_𝑐 − 𝑣𝑜𝑢𝑡_𝑎 ) + 𝑖𝑜𝑢𝑡_𝑐 (𝑣𝑜𝑢𝑡_𝑎 − 𝑣𝑜𝑢𝑡_𝑏 )]

(2.6)

(2.7)

The line-to-line RMS value of output voltage is calculated through (2.8) in the block “RMS”. 2 2 2 𝑉𝑜𝑢𝑡 = √𝑣𝑜𝑢𝑡_𝑎 + 𝑣𝑜𝑢𝑡_𝑏 + 𝑣𝑜𝑢𝑡_𝑐

(2.8)

The block “Governor Model” is an 𝜔 − 𝑃 droop controller, as shown in Fig. 2.5, where 𝜔0 is the nominal angular frequency, 𝑃0 is the set value of active power, 𝑘𝑝 is the 𝜔 − 𝑃 droop

Fig. 2.5

Block diagram of the “Governor Model” block of the basic VSG control.

Fig. 2.6

Block diagram of the “Q Droop” block of the basic VSG control.

- 16 -

Chapter 2 Principles of Virtual Synchronous Generator Control coefficient, and 𝑇𝑑 is the time constant of governor delay used to emulate the delayed mechanical response of a real governor of SG. The range of the output limiter for 𝑃𝑖𝑛 is –0.05 ~ 1.05 pu. Fig. 2.5 can be expressed as 𝑃𝑖𝑛 = 𝑃0 −

𝑘𝑝 (𝜔 − 𝜔0 ). 1 + 𝑇𝑑 𝑠 𝑚

(2.9)

The block “Q Droop” is an 𝑉 − 𝑄 droop controller, as shown in Fig. 2.6, where 𝐸0 is the nominal voltage, 𝑄0 is the set value of reactive power, and 𝑘𝑞 is the 𝑉 − 𝑄 droop coefficient. The range of the output limiter for 𝑄𝑟𝑒𝑓 is –1 ~ 1 pu. Fig. 2.6 can be expressed as 𝑄𝑟𝑒𝑓 = 𝑄0 − 𝑘𝑞 (𝑉𝑜𝑢𝑡 − 𝐸0 ).

(2.10)

The “Governor Model” block creates the linear droop control law between active power and the frequency, and the “Q Droop” block creates the linear droop control law between reactive power and the voltage. As this VSG control operates as a voltage source, it can be classified as a voltage-source-based grid-supporting control discussed in Section 1.2.2. That is to say, like other voltage-source-based grid-supporting controls, VSG-control-based inverter can operate individually, in parallel, and even be connected to the power grid directly, and no change of control is needed during operation mode transitions. Therefore, the VSG control can be considered as an upgraded voltage-source-based grid-supporting control which is able to provide inertia support. A Proportional-Integral (PI) controller is used to track the output reactive power to the reference value 𝑄𝑟𝑒𝑓 generated by the “Q Droop” controller. In order to diminish the influence from ripples in measured output power, a 20Hz first-order low-pass filter is applied for 𝑄𝑜𝑢𝑡 as shown in Fig. 2.2. As the output current is measured after the LC filter stage, the reactive power consumed by the LC filter is not included in 𝑄𝑜𝑢𝑡 . Therefore, no specific initial process is required for the reactive power PI controller. The output voltage of PWM inverter 𝑉𝑝𝑤𝑚 is obtained from the sum of the PI controller output and the nominal voltage 𝐸0 . The function of this PI controller is similar to the automatic reactive power regulators (AQR) of the SG, in which the electromotive force (emf) is controlled by regulating the field current. Therefore, the output voltage 𝑉𝑝𝑤𝑚 can be considered as the virtual internal emf 𝐸 of the VSG. It is noteworthy that inner current or voltage loop is not adopted in this control scheme, in order to make the filter inductor 𝐿𝑓 contribute to the output impedance and be considered as the stator inductance of the VSG (Note that the filter capacitor 𝐶𝑓 is usually negligible at fundamental frequency). This stator inductance results in more inductive output impedance, which is especially important for active and reactive power decoupling in a low voltage microgrid where line resistance is dominant. (Detailed discussion on the active and reactive power decoupling is presented in Section 3.3.1.) Nevertheless, output voltage is still regulated indirectly by the 𝑉 − 𝑄 droop controller and the PI controller of reactive power.

- 17 -

Chapter 2 Principles of Virtual Synchronous Generator Control

Contrarily, in conventional voltage-source-based grid-supporting control, usually an inner voltage loop is adopted; and in conventional current-source-based grid-supporting control, usually an inner current loop is adopted, as it is discussed in Section 3.2.1. In this case, the LC filter stage is the control plant of the inner voltage/current loop and cannot be counted into the output impedance. Therefore, the output impedance is purely the resistive line impedance. Although methods like virtual impedance have been proposed to address this issue, the output impedance design in conventional voltage/current-source-based grid-supporting control is more difficult than the VSG control. Detailed discussion on this point is presented in Section 4.4.

2.3.2 Per Unit Transformation In this dissertation, to simplify explications and to facilitate comparisons between inverters of different ratings, some control and hardware parameters are given in per unit values calculated based on respective power ratings of DGs. The moment of inertia 𝐽 is given in inertia constant 𝑀∗ (in second), defined as 𝑀∗ =

𝐽𝜔02 , 𝑆𝑏𝑎𝑠𝑒

(2.11)

where 𝑆𝑏𝑎𝑠𝑒 is the power rating of the DG. The damping factor 𝐷 is given in per unit value 𝐷 ∗, defined as 𝐷∗ =

𝐷𝜔0 , 𝑆𝑏𝑎𝑠𝑒

(2.12)

where superscript “∗” indicates per unit value. The 𝜔 − 𝑃 and 𝑉 − 𝑄 droop coefficients 𝑘𝑝 and 𝑘𝑞 are given in per unit values 𝑘𝑝∗ and 𝑘𝑞∗ , respectively, defined as 𝑘𝑝∗ =

𝑘𝑝 𝜔0 , 𝑆𝑏𝑎𝑠𝑒

(2.13)

𝑘𝑞∗ =

𝑘𝑞 𝐸0 . 𝑆𝑏𝑎𝑠𝑒

(2.14)

The set values of active and reactive power 𝑃0 and 𝑄0 are given in per unit values 𝑃0∗ and 𝑄0∗, respectively, defined as 𝑃0∗ =

𝑄0∗ =

𝑃0

,

(2.15)

𝑄0 . 𝑆𝑏𝑎𝑠𝑒

(2.16)

𝑆𝑏𝑎𝑠𝑒

- 18 -

Chapter 2 Principles of Virtual Synchronous Generator Control

In a microgrid, in order to share the active and reactive power according to the generator power ratings ratio without communication, 𝑘𝑝∗ , 𝑘𝑞∗ , 𝑃0∗ and 𝑄0∗ should be designed equally for each DG in default [4]. The PI controller is defined as (2.17) in this dissertation, and the PI gain 𝐾𝑝 is given in per unit value, which means the gain of output in per unit value over input in per unit value. The PI time constant 𝑇𝑖 is given in second. 𝐺(𝑠) = 𝐾𝑝 (1 +

1 ) 𝑇𝑖 𝑠

(2.17)

The per unit value of impedance 𝑍 = 𝑅 + 𝑗𝑋 is defined as follows. 𝑍∗ =

𝑍𝑆𝑏𝑎𝑠𝑒 , 𝐸02

(2.18)

𝑅∗ =

𝑅𝑆𝑏𝑎𝑠𝑒 , 𝐸02

(2.19)

𝑋∗ =

𝑋𝑆𝑏𝑎𝑠𝑒 , 𝐸02

(2.20)

where 𝑅, 𝑋 are the resistance and reactance, respectively.

2.3.3 Variations of Virtual Synchronous Generator Control Some variations of the basic VSG control have been proposed to improve the performance and/or address a specific issue. A study on parallel operation of VSGs is presented in [5]. A sophisticated damping method is presented in [6] to increase the active power damping during grid-connected mode under complicated line impedance condition. This problem is also addressed by the method of alternating moment of inertia [7]. Particle swarm optimization (PSO) is proposed to tune the parameter of VSGs in a microgrid consisting of multiple VSGs [8], and a modification of VSG for voltage sag ride-through is presented in [9]. Besides, VSG control can also be used to improve the performance of a traditional SG, as it is proposed in [10], in which VSG is applied to control the grid-side converter.

2.4 Other Existing Inverter Control Methods with Virtual Inertia The concept of VSG was originally proposed in [11] and has attracted a lot of attention from all over the world. Besides of the VSG control discussed in Section 2.3, several other control methods using virtual inertia have also been developed [12]. In this section, a brief survey of several typical examples is presented, and comparisons between these methods and the VSG control introduced in Section 2.3 are discussed.

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Chapter 2 Principles of Virtual Synchronous Generator Control

2.4.1 VSG Control Developed by VSYNC Project The VSYNC project under the 6th European Research Framework program is the first research team trying to use virtual inertia control for inverters [11], and their control methods have been developed through [13]–[22]. As the principle of VSYNC project is to regulate the grid frequency, their works focus more on the DESSs rather than DGs, as it is depicted in Fig. 2.7(a). It can be concluded that this control scheme is a current-source-based grid-supporting control as a current control loop is applied at the output terminal. A PLL unit is used to detect the frequency of the grid and to provide angle reference for the dq transformation. The detailed calculation of current reference based on active and reactive power reference is shown in Fig. 2.7(b). Compared with the basic VSG control discussed in Section 2.3, it can be noticed that the coefficient 𝐾𝑖𝑛𝑒𝑟𝑡𝑖𝑎 in Fig. 2.7(b) is analogous to the virtual inertia 𝐽 in (2.2), the coefficient 𝐾𝑓 is analogous to the 𝜔 − 𝑃

(a)

(b) Fig. 2.7

Typical VSG control scheme developed by VSYNC project [19].

(a) Overall control scheme. (b) Calculation of Reference Current.

- 20 -

Chapter 2 Principles of Virtual Synchronous Generator Control droop coefficient 𝑘𝑝 in (2.9) and the coefficient 𝐾𝑣 is analogous to the 𝑉 − 𝑄 droop coefficient 𝑘𝑞 in (2.10). A unique parameter 𝐾𝑠𝑜𝑐 is proposed to share the SOC between parallel DESSs. However, the damping factor is not included in this control scheme. Besides, this control scheme is not suitable for islanded operation without a voltage source reference.

2.4.2 VISMA Control Developed by IEPE Another inverter control method using virtual inertia is called virtual synchronous machine (VISMA) developed by the Institute of Electrical Power Engineering (IEPE), Clausthal University of Technology, Germany [23]–[28]. Two control methods of VISMA are proposed, one is a current-source-based method, and the other is a voltage-source-based method [27], as illustrated in Figs. 2.8 and 2.9, respectively. In current-source-based VISMA control, a hysteresis current controller is used to control the

(a)

(b) Fig. 2.8

Current-source-based VISMA control [27].

(a) Overall control scheme. (b) Model of synchronous machine 1.

- 21 -

Chapter 2 Principles of Virtual Synchronous Generator Control

(a)

(b) Fig. 2.9

Voltage-source-based VISMA control [27].

(a) Overall control scheme. (b) Model of synchronous machine 2.

output current, whereas the voltage-source-based VISMA control uses open-loop voltage source control. Stator impedance models including 𝐿𝑠 and 𝑅𝑠 are calculated in both control methods in an opposite way, and the mechanical parts in both control methods are the same. 𝑀𝑚𝑒𝑐ℎ , 𝑀𝑒𝑙 , and 𝑀𝑑 indicate the mechanical torque, electrical torque and the damping torque, respectively. The virtual inertia 𝐽 has the same function as that introduced in Section 2.3, but the damping power is emulated in a different way. As droop control laws are not included in both two VISMA control methods, both VISMA controls may not be suitable for parallel operation of inverters. In fact, the voltage-source-based VISMA control can be considered as an upgraded grid-forming control, and the current-source-based VISMA control can be considered as an upgraded grid-feeding control.

2.4.3 VSG Control Developed by KHI Kawasaki Heavy Industries (KHI) is also an active research group in the area of VSG control. KHI has developed VSG control for both three-phase and single-phase inverters [29]–[31]. The basic - 22 -

Chapter 2 Principles of Virtual Synchronous Generator Control

(a)

(b) Fig. 2.10

VSG control developed by KHI

(a) for a three-phase inverter [29], and (b) for a single-phase inverter [30].

VSG control scheme by KHI for a three-phase inverter is shown in Fig. 2.10(a) [29], and that for single-phase inverter is shown in Fig. 2.10(b) [30], which is an adapted version based on double decoupled synchronous reference frame (DDSRF) decomposition. As it is depicted in Fig. 2.10(a), the VSG control by KHI is based on dq transformation, in which the phase angle information is acquired by a PLL unit. The Govornor Model and AVR Model in Fig. 2.10(a) create the droop control laws, and a current control loop is presented at the output terminal. Therefore, the VSG control by KHI is a current-source-based grid-supporting control. It should be - 23 -

Chapter 2 Principles of Virtual Synchronous Generator Control

pointed out that the inputs and outputs of the droop control laws are opposite to the basic VSG control in Section 2.3, i.e. the inputs are active and reactive power and the outputs are frequency and voltage. In this type of droop control laws, a first-order delay can be used to emulate the inertia. Detailed discussion on this point is presented in Chapter 3. Besides, impedance model is also included in KHI’s VSG control, to emulate the stator impedance of a SG.

2.4.4 Synchronverter Another well-known inertial inverter control is called synchronverter, proposed by Prof. Q.-C. Zhong for three-phase inverter in [32], [33], and have been furtherly developed and applied in single-phase inverter [34], three-phase PWM rectifier [35], static synchronous compensator (STATCOM) [36], and HVDC system [37], [38]. The basic topology and control scheme of the original synchronverter for a three-phase inverter are shown in Fig. 2.11 [33]. The formulas of the electromagnetic torque 𝑒, the reactive power 𝑄 and the electromagnetic torque 𝑇𝑒 in the central block of Fig. 2.11(b) are as follows.

(a)

(b) Fig. 2.11

(a) Synchronverter topology and (b) synchronverter control scheme [33].

- 24 -

Chapter 2 Principles of Virtual Synchronous Generator Control

𝑒 = 𝜃̇ 𝑀𝑓 𝑖𝑓 sin ̃ 𝜃,

(2.21)

𝑇𝑒 = 𝑀𝑓 𝑖𝑓 〈𝑖, sin ̃ 𝜃〉,

(2.22)

𝑄 = −𝜃̇𝑀𝑓 𝑖𝑓 〈𝑖, cos ̃ 𝜃〉,

(2.23)

where 𝑖𝑓 is the field excitation current, 𝑀𝑓 is the maximum mutual inductance between the stator windings and the field winding. 𝜃̇ is the virtual angular speed of the machine and also the frequency of the control signal 𝑒 sent to the pulse width modulation (PWM) generator, and 𝑖 is the stator current (vector) flowing out of the machine. sin ̃ 𝜃 and cos ̃ 𝜃 are defined as sin 𝜃 2 sin(𝜃 − 𝜋) sin ̃𝜃 = , 3 2 [sin(𝜃 + 3 𝜋)]

(2.24)

cos 𝜃 2 cos(𝜃 − 𝜋) cos ̃𝜃 = . 3 2 [cos(𝜃 + 3 𝜋)]

(2.25)

The upper part of Fig. 2.11(b) can be expressed as 1 𝜃̈ = [𝑇𝑚 − 𝑇𝑒 − 𝐷𝑝 (𝜃̇ − 𝜃𝑟̇ )], 𝐽

(2.26)

where 𝑇𝑚 is the mechanical torque applied to the rotor, 𝐽 is the imaginary moment of inertia, 𝐷𝑝 is the mechanical friction coefficient and 𝜃𝑟̇ is the frequency reference. The principles of synchronverter are actually very similar to the basic VSG control introduced in Section 2.3, except that the damping power introduced by the damp winding is not emulated in the synchronverter control. The mechanical friction 𝐷𝑝 and voltage droop coefficient 𝐷𝑞 are analogous to the droop coefficients 𝑘𝑝 and 𝑘𝑞 in Section 2.3, respectively. Therefore, the synchronverter control is also a voltage-source-based grid-supporting control method.

2.4.5 Other Typical Virtual Inertia Control Methods Besides of abovementioned research groups, several other virtual inertia control methods have been developed. Similar to the VSYNC project, some researchers focus on the kinetic energy only and therefore propose virtual inertia control methods for DESSs [39]–[40]. Some virtual inertia control methods for inverter-interfaced DGs are based on modifications on droop control, e.g. adding a first-order delay [41], [42] or modifying the 𝑃 − 𝜔 droop coefficient [43]. However, in [41], [42], the angular frequency of the bus 𝜔𝑔 , which provides the synchronous frequency for damping power calculation in (2.2), is replaced by a constant value, i.e., nominal frequency 𝜔0, thus the damping - 25 -

Chapter 2 Principles of Virtual Synchronous Generator Control factor 𝐷 becomes equivalent to droop coefficient 𝑘𝑝 . This modification of swing equation results in a simpler model, and as a result, the dedicated governor can even be omitted, as it is presented in [42]. In this case, however, no damping effect caused by damper winding is emulated, which may result in larger output power oscillation.

2.5 Conclusion In this chapter, principles of VSG controls were introduced. The basic VSG control developed by Ise Laboratory was presented in detail, and other inverter control methods providing virtual inertia were briefly reviewed.

References [1]

J. Machowski, J. Bialek, and J. R. Bumby, Power System Dynamics and Stability. New York: John Wiley & Sons, 1997, pp. 141–182.

[2]

K. Sakimoto, Y. Miura, and T. Ise, “Stabilization of a power system including inverter type distributed generators by the virtual synchronous generator,” IEEJ Trans. Power and Energy, vol. 132, no. 4, pp. 341–349, Apr. 2012 (in Japanese). or Electrical Engineering in Japan, vol. 187, no. 3, pp. 7–17, May 2014 (in English).

[3]

T. Shintai, Y. Miura, and T. Ise, “Reactive power control for load sharing with virtual synchronous generator control,” in Proc. 7th Int. Power Electron. Motion Control Conf., 2012, pp. 846–853.

[4]

J. Rocabert, A. Luna, F. Blaabjerg, and P. Rodríguez, “Control of power converters in AC microgrids,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4734–4749, Nov. 2012.

[5]

K. Sakimoto, Y. Miura, and T. Ise, “Characteristics of parallel operation of inverter-type distributed generators operated by a virtual synchronous generator,” IEEJ Trans. Power and Energy, vol. 133, no. 2, pp. 186–194, Feb. 2013 (in Japanese). or Electrical Engineering in Japan, vol. 192, no. 4, pp. 9–19, Sep. 2015 (in English).

[6]

T. Shintai, Y. Miura, and T. Ise, “Oscillation damping of a distributed generator using a virtual synchronous generator,” IEEE Trans. Power Del., vol. 29, no. 2, pp. 668–676, Apr. 2014.

[7]

J. Alipoor, Y. Miura, and T. Ise, “Power system stabilization using virtual synchronous generator with alternating moment of inertia,” IEEE J. Emerg. Sel. Topics Power Electron., vol. 3, no. 2, pp. 451–458, Jun. 2015.

[8]

J. Alipoor, Y. Miura, and T. Ise, “Optimazation of microgrid with multiple VSG units,” 電気 学 会 電 力 技 術 ・ 電 力 系 統 技 術 合 同 研 究 会 , PE–14–125 , PSE–14–125 , pp.51–56 (2014).

[9]

J. Alipoor, Y. Miura, and T. Ise, “Voltage sag ride-through performance of Virtual Synchronous Generator,” in Proc. Int. Power Electron. Conf. (IPEC-Hiroshima ECCE-Asia), 2014, pp. 3298–3305.

- 26 -

Chapter 2 Principles of Virtual Synchronous Generator Control [10] Y., Banjo, Y. Miura, T. Ise, and T. Shintai, “Enhanced stand-alone operating characteristics of an engine generator interconnected through the inverter using virtual synchronous generator control,” in Proc. Int. Conf. Power Electron., 2015, pp.1003–1010. [11] J. Driesen and K. Visscher “Virtual synchronous generators,” in Proc. IEEE Power Energy Soc. Gen. Meeting—Convers. Del. Elect. Energy 21st Century, 2008, pp. 1–3. [12] H. Bevrani, T. Ise, and Y. Miura, “Virtual synchronous generators: A survey and new perspectives,” Int. J. Elect. Power Energy Syst., vol. 54, no. 1, pp. 244–254, Jan. 2014. [13] K. Visscher and S. W. H. de Haan, “Virtual synchronous machines (VSG’s) for frequency stabilisation in future grids with a significant share of decentralized generation,” in Proc. IET-CIRED Seminar SmartGrids for Distribution, 2008, pp. 1–4. [14] M.P.N. van Wesenbeeck, S.W.H. de Haan, P. Varela, and K. Visscher, “Grid tied converter with virtual kinetic storage,” in Proc. IEEE Bucharest PowerTech, 2009, pp.1–7. [15] T. Loix, S. de Breucker, P. Vanassche, J. van den Keybus, J. Driesen, and K. Visscher, “Layout and performance of the power electronic converter platform for the VSYNC project,” in Proc. IEEE Bucharest PowerTech, 2009, pp. 1–8. [16] M. Albu, K. Visscher, D. Creanga, A. Nechifor, and N. Golovanov, “Storage selection for DG applications containing virtual synchronous generators,” in Proc. IEEE Bucharest PowerTech, 2009, pp.1–6. [17] T. Vu Van, A. Woyte, M. Albu, M. van Hest, J. Bozelie, J. Diaz, T. Loix, D. Stanculescu, and K. Visscher, “Virtual synchronous generator: Laboratory scale results and field demonstration,” in Proc. IEEE Bucharest PowerTech, 2009, pp.1–6. [18] M. Albu, J. Diaz, V. Thong, R. Neurohr, D. Federenciuc, M. Popa, and M. Calin, “Measurement and remote monitoring for virtual synchronous generator design,” in Proc. IEEE Int. Workshop Appl. Measurements for Power Syst., 2010, pp.7–11. [19] V. Karapanos, Z. Yuan, and S. W. H. de Haan, “SOC maintenance and coordination of multiple VSG units for grid support and transient stability,” presented at the 3rd VSYNC workshop,

Cheia,

Romania,

2010.

[Online].

Available:

http://www.vsync.eu/fileadmin/vsync/user/docs/ Workshop3/Karapanos.pdf [20] M. Albu, M. Calin, D. Federenciuc, and J. Diaz, “The measurement layer of the Virtual Synchronous Generator operation in the field test,” in Proc. IEEE Int. Workshop Appl. Measurements for Power Syst., 2011, pp.85–89. [21] V. Karapanos, S. W. H. de Haan, and K. H. Zwetsloot, “Testing a virtual synchronous generator in a real time simulated power system,” in Proc. Int. Conf. Power Syst. Transients, 2011. [22] V. Karapanos, S. W. H. de Haan, and K. H. Zwetsloot, “Real time simulation of a power system with VSG hardware in the loop," in Proc. Annu. Conf. IEEE Ind. Electron. Soc., 2011, pp. 3748–3754.

- 27 -

Chapter 2 Principles of Virtual Synchronous Generator Control [23] H.-P. Beck and R. Hesse, “Virtual synchronous machine,” in Proc. Int. Conf. Elect. Power Quality and Utilisation, 2007, pp. 1–6. [24] R. Hesse, D. Turschner, and H.-P. Beck, “Micro grid stabilization using the virtual synchronous machine (VISMA),” in Proc. Int. Conf. Renewable Energies and Power Quality, 2009, pp. 1–6. [25] Y. Chen, R. Hesse, D. Turschner, and H.-P. Beck, “Dynamic properties of the virtual synchronous machine (VISMA),” in Proc. Int. Conf. Renewable Energies and Power Quality, 2011, pp. 1–5. [26] Y. Chen, R. Hesse, D. Turschner, and H.-P. Beck, “Improving the grid power quality using virtual synchronous machines,” in Proc. Int. Conf. Power Eng., Energy and Elect. Drives, 2011, pp.1–6. [27] Y. Chen, R. Hesse, D. Turschner, and H.-P. Beck, “Comparison of methods for implementing virtual synchronous machine on inverters,” in Proc. Int. Conf. Renewable Energies and Power Quality, 2012, pp. 1–6. [28] Y. Chen, R. Hesse, D. Turschner, and H.-P. Beck, “Investigation of the Virtual Synchronous Machine in the island mode,” in Proc. IEEE PES Int. Conf. and Exhibition on Innovative Smart Grid Technologies, 2012, pp.1–6. [29] Y. Hirase, A. Kazuhiro, K. Sugimoto, and Y. Shindo, “A grid-connected inverter with virtual synchronous generator model of algebraic type,” IEEJ Trans. Power and Energy, vol. 132, no. 4, pp. 371–380, Apr. 2012 (in Japanese). or Electrical Engineering in Japan, vol. 184, no. 4, pp. 10–21, Sep. 2013 (in English). [30] Y. Hirase, O. Noro, E. Yoshimura, H. Nakagawa, K. Sakimoto, and Y. Shindo, “Virtual synchronous generator control with double decoupled synchronous reference frame for single-phase inverter,” IEEJ J. Ind. Appl., vol. 4, no. 3, pp. 143–151, May 2015. [31] Y. Hirase, O. Noro, K. Sugimoto, K. Sakimoto, Y. Shindo, and T. Ise, “Effects of suppressing frequency fluctuations by parallel operation of virtual synchronous generator in microgrids,” in Proc. IEEE Energy Convers. Congr. and Expo., 2015, pp. 3694–3701. [32] Q.-C. Zhong and G. Weiss, “Synchronverters: inverters that mimic synchronous generators,” IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1259–1267, Apr. 2011. [33] Q.-C. Zhong, P.-L. Nguyen, Z. Ma, and W. Sheng, “Self-synchronized synchronverters: inverters without a dedicated synchronization unit,” IEEE Trans. Power Electron., vol. 29, no. 2, pp. 617–630, Feb. 2014. [34] W.-L. Ming and Q.-C. Zhong, “Synchronverter-based transformerless PV inverters,” in Proc. Annu. Conf. IEEE Ind. Electron. Soc., 2014, pp. 4396–4401. [35] Z. Ma; Q.-C. Zhong, and J. D. Yan, “Synchronverter-based control strategies for three-phase PWM rectifiers in Proc. IEEE Conf. on Ind. Electron. and Appl., 2012, pp. 225–230.

- 28 -

Chapter 2 Principles of Virtual Synchronous Generator Control [36] P.-L. Nguyen, Q.-C. Zhong, F. Blaabjerg, and J.M. Guerrero, “Synchronverter-based operation of STATCOM to mimic synchronous condensers,” in Proc. IEEE Conf. on Ind. Electron. and Appl., 2012, pp. 942–947. [37] R. Aouini, B. Marinescu, K. Ben Kilani, and M. Elleuch, “Synchronverter-based emulation and control of HVDC transmission,” IEEE Trans. Power Syst., vol. 31, no. 1, pp. 278–286, Jan. 2016. [38] S. Dong, Y.-N. Chi, and Y. Li, “Active voltage feedback control for hybrid multi-terminal hvdc system adopting improved synchronverters,” IEEE Trans. Power Del., doi: 10.1109/ TPWRD.2015.2420657. [39] G. Delille, B. Francois, and G Malarange, “Dynamic frequency control support by energy storage to reduce the impact of wind and solar generation on isolated power system's inertia,” IEEE Trans. Sustain. Energy, vol. 3, no. 4, pp. 931–939, Oct. 2012. [40] M. A. Torres L., L. A. C. Lopes, L. A. Moran T., and J. R. Espinoza C., “Self-tuning virtual synchronous machine: A control strategy for energy storage systems to support dynamic frequency control,” IEEE Trans. Energy Convers., vol. 29, no. 4, pp. 833–840, Dec. 2014. [41] M. Guan, W. Pan, J. Zhang, Q. Hao, J. Cheng, and X. Zheng, “Synchronous generator emulation control strategy for voltage source converter (VSC) stations,” IEEE Trans. Power Syst., vol. 30, no. 6, pp. 3093–3101, Nov. 2015. [42] Y. Du, J. M. Guerrero, L. Chang, J. Su, and M. Mao, “Modeling, analysis, and design of a frequency-droop-based virtual synchronous generator for microgrid applications,” in Proc. IEEE ECCE Asia Downunder, 2013, pp. 643–649. [43] N. Soni, S. Doolla, and M. C. Chandorkar, “Improvement of transient response in microgrids using virtual inertia,” IEEE Trans. Power Del., vol. 28, no. 3, pp. 1830–1838, Jul. 2013.

- 29 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control 3.1 Introduction In this chapter, a comprehensive comparison of dynamic characteristics between droop control and VSG control is presented, in order to understand the difference of the two control methods caused by the presence of swing equation, and the advantage and disadvantage of VSG control over traditional voltage-source-based grid-supporting control [1], [2]. Small-signal models of both methods are built, for the case of single inverter operation and that of parallel operation with a SG, to calculate theoretical step responses of frequency change, in order to understand the inertia effect caused by the virtual inertia. Effects of delays in governor of VSG and P droop controller of droop control are also evaluated, and an approximated VSG control based on droop control, i.e. inertial droop control, is proposed. State-space models of both methods are constructed to study oscillation of output active power. Theoretical results are verified by simulations using PSCAD/EMTDC and by experiments of a scale-down system. Comparison between droop control and VSG control in a VSC-HVDC transmission system is demonstrated in [3], to show that the virtual inertia helps to reduce maximum frequency excursion during a short-time fault, and during loading transition when secondary frequency control is applied; however, detailed theoretical analysis is not provided. A comparison on transient active power performance is presented in [4], but the differences on inertia and transient frequency are not discussed. Moreover, although the idea of using a first-order lag unit in droop control to emulate virtual inertia is already mentioned in [3], [4], it is further developed in this dissertation by adding a first-order lag unit to emulate the damping factor. It should be pointed out that although the VSG control scheme studied in this chapter is based on the basic VSG control introduced in Section 2.3, several results should also be valid for other voltage-source-based grid-supporting control with virtual inertia. Moreover, the small-signal models and state-space models presented in this chapter provide a general method for analyses of dynamic performances of VSG and droop control, which smooth the path of future studies on this topic. Actually, several improvements and modifications on VSG control proposed in Chapters 4 and 5 are based on the state-space analyses presented in this chapter.

- 30 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

3.2 Droop Control 3.2.1 Overview of Droop Control Droop control is a control method for real and reactive power regulation by imitating the parallel operation characteristics of synchronous generators (SGs). It is initially proposed for uninterruptible power supply (UPS) systems [5], and has been developed into a general approach for parallel inverters [6], especially in microgrids [7]–[33] and UPS systems [34], [35]. There are several variants of droop control. To be applied in low voltage (LV) network, in which the line impedance is mainly resistive, 𝑃 − 𝑉 and 𝑄 − 𝜔 droop control [8]–[11], instead of traditional 𝑃 − 𝜔 and 𝑄 − 𝑉 droop [5]–[7], has been proposed to improve power sharing and stability. Moreover, a virtual frequency-voltage frame method is proposed to solve this problem in any giving condition of line impedance 𝑅/𝑋 ratio [12]. On the other hand, 𝑃 − 𝜔 and 𝑄 − 𝑉 droop can still be applied in LV network by adding virtual output impedance to make the total line impedance inductive [14]–[16], [34], [35]. In a hierarchical microgrid control structure, droop control usually plays the role of primary control, in which secondary control is designed to keep the frequency and voltage around the nominal value [13]–[18], and/or to obtain accurate reactive power [17]–[22], harmonic and unbalance power sharing [20] and voltage harmonic compensation [18], [23] in islanded mode, and tertiary control is designed to manage synchronization to the main grid, power-flow control in grid-connected mode and optimal operation [15], [16]. As secondary and tertiary control need communication command from a central controller, issues are still encouraged to be solved with a wireless manner, such as it is proposed in [23]–[28] for accurate power sharing, in [29] for operation with unbalance load and nonlinear load, in [30] for harmonic components dispatch, and in [31] for reducing frequency and voltage deviation. It has also been demonstrated that optimization of droop coefficients [32] and supplementary droop control loop [33] can help to enhance system stability. As current-source-based droop control cannot provide voltage support for islanded microgrid, most droop control methods proposed in the literature are voltage-source-based droop control. A typical voltage-source-based droop control using 𝑃 − 𝜔 and 𝑄 − 𝑉 is depicted in Fig. 3.1. The blocks “P Droop” and “Q Droop”, as shown in Figs. 3.2 and 3.3, are based on 𝑃 − 𝜔 and 𝑄 − 𝑉 droop control laws, respectively. The input of the droop controller is the output active and reactive power 𝑃𝑜𝑢𝑡 and 𝑄𝑜𝑢𝑡 calculated from output voltage and current, and the output is the output frequency 𝜔𝑚 and output voltage reference 𝑉𝑟𝑒𝑓 . The first lag unit with a time constant 𝑇𝑑 is used to filter the high frequency ripples in the calculated 𝑃𝑜𝑢𝑡 and 𝑄𝑜𝑢𝑡 The relations shown in Figs. 3.2 and 3.3 can be expressed as (3.1) and (3.2), respectively. 𝜔𝑚 = −

𝑃𝑜𝑢𝑡 − 𝑃0 + 𝜔0 𝑘𝑝 (1 + 𝑇𝑑 𝑠)

- 31 -

(3.1)

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.1

Block diagram of the conventional voltage-source-based droop control scheme.

Fig. 3.2

Block diagram of the “P Droop” block of conventional droop control.

Fig. 3.3

Block diagram of the “Q Droop” block of conventional droop control.

𝑉𝑟𝑒𝑓 = −

𝑄𝑜𝑢𝑡 − 𝑄0 + 𝐸0 𝑘𝑞 (1 + 𝑇𝑑 𝑠)

(3.2)

Compared with the “Governor Model” and “Q Droop” controller of the basic VSG control (Figs. 2.5 and 2.6), it can be observed that the input and output are inversed. The difference between 𝑃 − 𝜔 droop and 𝜔 − 𝑃 droop is discussed in Section 3.3.3, and difference between 𝑄 − 𝑉 droop and 𝑉 − 𝑄 droop is discussed in Section 4.3 of next chapter. The block “Voltage Control” is used to control the amplitude of output voltage to the voltage reference value 𝑉𝑟𝑒𝑓 . There are a variety of choices for the control method inside the “Voltage Control” block. It can be either a single voltage loop control [7] or a multi-loop control composed of an outer voltage loop and an inner current loop [11]-[13]. Nevertheless, detailed discussion on the voltage controller of droop control is beyond the scope of this dissertation.

- 32 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

3.2.2 Principles of Active Control Part of VSG Control and Droop Control In this chapter, to simplify the model in order to focus on active power control, reactive power control parts of both VSG control and droop control are inactivated. Therefore, the output voltage of inverter 𝐸 is fixed to the nominal voltage 𝐸0 , as illustrated in Figs. 3.4 and 3.5. Detailed discussion on reactive power control part is presented in Section 4.3 of next chapter. From (2.2) and (2.9), the active power control of VSG control can be expressed in a single equation by eliminating 𝑃𝑖𝑛 , as shown in (3.3). 𝑃0 −

𝑘𝑝 d𝜔𝑚 (𝜔𝑚 − 𝜔0 ) − 𝑃𝑜𝑢𝑡 = 𝐽𝜔𝑚 + 𝐷(𝜔𝑚 − 𝜔𝑔 ) 1 + 𝑇𝑑 𝑠 d𝑡

(3.3)

It is simpler to neglect the effect of first-order delay at the beginning of the comparison. There-

Fig. 3.4

Simplified VSG control without reactive power control.

Fig. 3.5

Simplified droop control without reactive power control.

- 33 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

fore, (3.3) and (3.1) can be simplified as (3.4) and (3.5), respectively. 𝑃0 − 𝑘𝑝 (𝜔𝑚 − 𝜔0 ) − 𝑃𝑜𝑢𝑡 = 𝐽𝜔𝑚

𝜔𝑚 = −

d𝜔𝑚 + 𝐷(𝜔𝑚 − 𝜔𝑔 ) d𝑡

𝑃𝑜𝑢𝑡 − 𝑃0 + 𝜔0 𝑘𝑝

(3.4)

(3.5)

Letting 𝐽 = 0, 𝐷 = 0, (3.4) is equivalent to (3.5). In other words, droop control can be considered as a particular case of VSG control, in which both inertia and damping factor are set to zero.

3.3 Comparisons of Transient Responses of Frequency In this section, first, small-signal models of VSG and droop control are built for both single inverter operation and parallel operation with a SG. Then, based on these models, step responses of frequency change during a loading transition are calculated. The system with slower change of frequency is preferable, because lower d𝑓/d𝑡 indicates larger inertia. System with smaller inertia is prone to exceed the d𝑓/d𝑡 threshold of relays during a large loading transition, which may lead to unnecessary tripping and load shedding. Moreover, system with larger inertia suffers smaller maximum frequency excursion during a short time fault, and during a loading transition when secondary control is applied, as it is demonstrated in [3].

3.3.1 Single Inverter Operation First of all, single inverter operation model shown in Fig. 3.6 is studied. The capacitor of the DG output filter shown in Figs. 3.4 and 3.5 is neglected as its susceptance is usually negligible at fundamental frequency. The power flow 𝑆𝑒_𝑑𝑔 out of the virtual internal emf 𝐸𝑑𝑔 ∠𝛿𝑑𝑔 can be expressed as 𝑆𝑒_𝑑𝑔 = 𝑃𝑒_𝑑𝑔 + 𝑗𝑄𝑒_𝑑𝑔 =

𝐸𝑑𝑔 2 [𝑅𝑑𝑔 (𝐸𝑑𝑔 − 𝑉𝑏𝑢𝑠 cos𝛿𝑑𝑔 ) + 𝑋𝑑𝑔 𝑉𝑏𝑢𝑠 sin𝛿𝑑𝑔 ] + 𝑋𝑑𝑔

2 𝑅𝑑𝑔

𝐸𝑑𝑔 +𝑗 2 2 [−𝑅𝑑𝑔 𝑉𝑏𝑢𝑠 sin𝛿𝑑𝑔 + 𝑋𝑑𝑔 (𝐸𝑑𝑔 − 𝑉𝑏𝑢𝑠 cos𝛿𝑑𝑔 )], 𝑅𝑑𝑔 + 𝑋𝑑𝑔

Fig. 3.6

System model of the case of single inverter operation.

- 34 -

(3.6)

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control where subscript “dg” indicates parameters related to DG, 𝑋𝑑𝑔 = 𝑋𝑓_𝑑𝑔 + 𝑋𝑙𝑖𝑛𝑒_𝑑𝑔 and 𝑅𝑑𝑔 ≈ 𝑅𝑙𝑖𝑛𝑒_𝑑𝑔 are the total output reactance and resistance of DG, respectively, 𝑉𝑏𝑢𝑠 is the RMS value of bus voltage, 𝛿𝑑𝑔 is the power angle of DG (angle difference between the virtual internal emf and bus voltage). Equation (3.6) can be simplified to (3.7) if 𝑅𝑑𝑔 ≪ 𝑋𝑑𝑔 . It is always the case in high voltage (HV) network because a transmission line is mainly inductive. In low voltage (LV) network where distribution line is mainly resistive, the filter inductance 𝑋𝑓_𝑑𝑔 is usually large enough to make the output impedance inductive. Even it is not the case, the total output impedance can be adjusted to be inductive by the stator impedance adjuster presented in Section 4.4. 𝑆𝑒_𝑑𝑔 = 𝑃𝑒_𝑑𝑔 + 𝑗𝑄𝑒_𝑑𝑔 =

𝐸𝑑𝑔 𝑉𝑏𝑢𝑠 sin𝛿𝑑𝑔 𝐸𝑑𝑔 (𝐸𝑑𝑔 − 𝑉𝑏𝑢𝑠 cos𝛿𝑑𝑔 ) +𝑗 𝑋𝑑𝑔 𝑋𝑑𝑔

(3.7)

If the power loss in the power devices of inverter and in the output LC filter is neglected, 𝑃𝑒_𝑑𝑔 ≈ ed, 𝑃𝑒_𝑑𝑔 ≈ 𝑃𝑜𝑢𝑡_𝑑𝑔 . Therefore, the small-signal relation of ∆𝑃𝑜𝑢𝑡_𝑑𝑔 can be deduced from (3.7) as ∆𝑃𝑜𝑢𝑡_𝑑𝑔 =𝐾𝑑𝑔 ∆𝛿𝑑𝑔 ,

(3.8)

𝐸𝑑𝑔 𝑉𝑏𝑢𝑠 cos𝛿𝑑𝑔 𝑋𝑑𝑔

(3.9)

where 𝐾𝑑𝑔 =

is the transient synchronizing power coefficient of the DG. For an inverter-interfaced DG, the power angle 𝛿𝑑𝑔 is usually small and cos𝛿𝑑𝑔 ≈ 1. Knowing that 𝑠∆𝛿𝑑𝑔 = ∆𝜔𝑚_𝑑𝑔 − ∆𝜔𝑔 , so that (3.8) becomes 𝑠∆𝑃𝑜𝑢𝑡_𝑑𝑔 ≈ 𝐾𝑑𝑔 (∆𝜔𝑚_𝑑𝑔 − ∆𝜔𝑔 ).

(3.10)

The small-signal model of (3.4) can be written as 2 −𝑘𝑝_𝑑𝑔 ∆𝜔𝑚_𝑑𝑔 − ∆𝑃𝑜𝑢𝑡_𝑑𝑔 = 𝐽𝑑𝑔 (𝜔𝑚_𝑑𝑔 𝑠∆𝜔𝑚_𝑑𝑔 + 𝑠∆𝜔𝑚_𝑑𝑔 ) + 𝐷𝑑𝑔 (∆𝜔𝑚_𝑑𝑔 − ∆𝜔𝑔 ).

(3.11)

As the frequency deviation from nominal frequency is relatively small, 𝜔𝑚_𝑑𝑔 𝑠∆𝜔𝑚_𝑑𝑔 ≈ 𝜔0 𝑠∆𝜔𝑚_𝑑𝑔 . Moreover, second order perturbation terms can be neglected. Therefore, (3.11) becomes −𝑘𝑝_𝑑𝑔 ∆𝜔𝑚_𝑑𝑔 − ∆𝑃𝑜𝑢𝑡_𝑑𝑔 = 𝐽𝑑𝑔 𝜔0 𝑠∆𝜔𝑚_𝑑𝑔 + 𝐷𝑑𝑔 (∆𝜔𝑚_𝑑𝑔 − ∆𝜔𝑔 ).

(3.12)

If line losses are neglected, ∆𝑃𝑜𝑢𝑡_𝑑𝑔 = ∆𝑃𝑙𝑜𝑎𝑑 , where 𝑃𝑙𝑜𝑎𝑑 is the active power consumed by the load. Eliminating ∆𝜔𝑔 from (3.10) and (3.12) gives 𝐷𝑑𝑔 1+ 𝑠 ∆𝜔𝑚_𝑑𝑔 𝐾𝑑𝑔 =− . ∆𝑃𝑙𝑜𝑎𝑑 𝑘𝑝_𝑑𝑔 + 𝐽𝑑𝑔 𝜔0 𝑠

- 35 -

(3.13)

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Equation (3.13) is the transfer function of frequency change over a small loading transition for a VSG-control-based DG in the case of single inverter operation. Let 𝐽𝑑𝑔 = 0, 𝐷𝑑𝑔 = 0, and then the transfer function for a droop-control-based DG can be obtained as follows. ∆𝜔𝑚_𝑑𝑔 1 =− ∆𝑃𝑙𝑜𝑎𝑑 𝑘𝑝_𝑑𝑔

(3.14)

Let 𝑠 = 0 in (3.13), and then (3.13) is equivalent to (3.14). This implies that steady-state gain of (3.13) is determined by droop coefficient 𝑘𝑝_𝑑𝑔 and is independent of swing equation parameters. In other words, steady states of VSG control and droop control are the same if droop coefficients 𝑘𝑝_𝑑𝑔 are set equally. It is possible to calculate the step responses of DG frequency change during a small loading transition through (3.13) and (3.14), as illustrated in Fig. 3.7. Parameters used for calculation are listed in Table 3.1. It is shown in Fig. 3.7 that the frequency of VSG control changes slowly, whereas that of droop control suffers a step change. This implies that DG with VSG control has inertia thanks to the swing equation, and that DG with droop control has nearly no inertia. Moreover, larger value of 𝐽𝑑𝑔 results in slower frequency change, which indicates that inertia of the DG is determined by 𝐽𝑑𝑔 . On the other hand, 𝐷𝑑𝑔 has barely any influence on dynamic response in this situation. Besides, steady states of all cases are the same. This verifies previous conclusion that steady states only de-

Fig. 3.7

Step responses of DG frequency during a loading transition in the case of single inverter operation with various parameters.

TABLE 3.1

Parameters of the Case of Single Inverter Operation

Parameter

Value

Parameter

Value

𝐸𝑑𝑔 = 𝐸0

6.6 kV

∗ 𝑘𝑝_𝑑𝑔

20 pu

𝑆𝑏𝑎𝑠𝑒_𝑑𝑔

1 MVA

∗ 𝑋𝑓_𝑑𝑔

0.1298 pu

∗ 𝑃0_𝑑𝑔

1 pu

∗ 𝑋𝑙𝑖𝑛𝑒_𝑑𝑔

0.0076 pu

𝜔0

376.99 rad/s

cos𝛿𝑑𝑔

≈1

𝑀0∗

8s

𝑉𝑏𝑢𝑠

6.57 kV

𝐷0∗

17 pu

∆𝑃𝑙𝑜𝑎𝑑

0.0095 MW

- 36 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control pend on 𝑘𝑝_𝑑𝑔 .

3.3.2 Parallel Operation with a SG In this section, parallel operation of DG and SG illustrated in Fig. 3.8 is studied to show the importance of inertia in a network with high penetration level of inverter-interfaced DG. It is assumed that the penetration rate of DG in this network is up to 50%, and the rest of power generation comes from a salient-pole SG. In this case, it is preferred to study the rotor frequency change of SG rather than that of DG because the former is considered as the dominant one. From the law of conservation of energy, ∆𝑃𝑜𝑢𝑡_𝑑𝑔 + ∆𝑃𝑜𝑢𝑡_𝑠𝑔 = ∆𝑃𝑙𝑜𝑎𝑑 ,

where subscript “sg” indicates parameters related to SG. Let 𝐴 =

(3.15) ∆𝑃𝑜𝑢𝑡_𝑑𝑔 ∆𝜔𝑔

and 𝐵 =

∆𝑃𝑜𝑢𝑡_𝑠𝑔 ∆𝜔𝑔

, so that

(3.15) becomes 𝐴 ∆𝑃𝑜𝑢𝑡_𝑠𝑔 (1 + ) = ∆𝑃𝑙𝑜𝑎𝑑 . 𝐵

(3.16)

The same equation as (3.10) holds for SG, as shown in (3.17). 𝑠∆𝑃𝑜𝑢𝑡_𝑠𝑔 ≈ 𝐾𝑠𝑔 (∆𝜔𝑚_𝑠𝑔 − ∆𝜔𝑔 )

(3.17)

Eliminate ∆𝑃𝑜𝑢𝑡_𝑠𝑔 from (3.16) and (3.17), so that ∆𝜔𝑚_𝑠𝑔 𝐾𝑠𝑔 + 𝐵𝑠 = . ∆𝑃𝑙𝑜𝑎𝑑 𝐾𝑠𝑔 (𝐴 + 𝐵)

(3.18)

Now if 𝐴 and 𝐵 are known, the required transfer function can be obtained. Eliminate ∆𝜔𝑚_𝑑𝑔 from (3.10) and (3.12), and then 𝐴=

Fig. 3.8

∆𝑃𝑜𝑢𝑡_𝑑𝑔 =− ∆𝜔𝑔

𝑘𝑝_𝑑𝑔 + 𝐽𝑑𝑔 𝜔0 𝑠 . 𝑘𝑝_𝑑𝑔 + 𝐷𝑑𝑔 𝐽𝑑𝑔 𝜔0 2 1+ 𝑠+ 𝑠 𝐾𝑑𝑔 𝐾𝑑𝑔

System model of the case of parallel operation with a SG.

- 37 -

(3.19)

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Because SG has the same model as VSG, (3.19) is also true for SG, as shown in (3.20). 𝐵=

∆𝑃𝑜𝑢𝑡_𝑠𝑔 =− ∆𝜔𝑔

𝑘𝑝_𝑠𝑔 + 𝐽𝑠𝑔 𝜔0 𝑠 𝑘𝑝_𝑠𝑔 + 𝐷𝑠𝑔 𝐽𝑠𝑔 𝜔0 2 1+ 𝑠+ 𝑠 𝐾𝑠𝑔 𝐾𝑠𝑔

(3.20)

Let 𝐽𝑑𝑔 = 0, 𝐷𝑑𝑔 = 0 in (3.19), and then 𝐴 for droop control can be obtained as 𝐴=

∆𝑃𝑜𝑢𝑡_𝑑𝑔 =− ∆𝜔𝑔

𝑘𝑝_𝑑𝑔 . 𝑘𝑝_𝑑𝑔 1+ 𝑠 𝐾𝑑𝑔

(3.21)

Remember that for SG, 𝐾𝑠𝑔 and 𝐷𝑠𝑔 are not constant and are dependent on the power angle 𝛿𝑠𝑔 and SG impedance parameters. 𝐷𝑠𝑔 can be calculated through (2.3) and 𝐾𝑠𝑔 can be calculated as follows for a salient-pole SG [36]. 𝐾𝑠𝑔 =

𝐸′𝑞 𝑉𝑏𝑢𝑠 𝑉𝑏𝑢𝑠 2 (𝑋𝑞 − 𝑋 ′ 𝑑 ) cos 𝛿𝑠𝑔 − cos(2𝛿𝑠𝑔 ), 𝑋′𝑑 + 𝑋𝑙𝑖𝑛𝑒_𝑠𝑔 (𝑋𝑞 + 𝑋𝑙𝑖𝑛𝑒_𝑠𝑔 )(𝑋 ′ 𝑑 + 𝑋𝑙𝑖𝑛𝑒_𝑠𝑔 )

(3.22)

where 𝑋𝑞 is the q-axis synchronous reactance of the SG, 𝐸′𝑞 is the q-axis transient internal emf. In order to verify the results through simulation lately, all parameters need to be measurable. Actually, all parameters in (2.3) and (3.22) except power angle 𝛿𝑠𝑔 , transient internal emf 𝐸′𝑞 and bus voltage 𝑉𝑏𝑢𝑠 are fixed SG parameters which can be found in data sheets. Besides, 𝑉𝑏𝑢𝑠 can be measured directly, while 𝛿𝑠𝑔 and 𝐸′𝑞 can be calculated through (3.23) and (3.24) with the measurement of the amplitude of SG output current 𝐼𝑠𝑔 and the angle 𝜑𝑠𝑔 which is the phase difference between 𝑽𝒃𝒖𝒔 and 𝑰𝒔𝒈 as shown in Fig. 3.8. 𝛿𝑠𝑔 = tan−1

(𝑋𝑞 + 𝑋𝑙𝑖𝑛𝑒_𝑠𝑔 )𝐼𝑠𝑔 cos 𝜑𝑠𝑔 𝑉𝑏𝑢𝑠 + (𝑋𝑞 + 𝑋𝑙𝑖𝑛𝑒_𝑠𝑔 )𝐼𝑠𝑔 sin 𝜑𝑠𝑔

𝐸′𝑞 = 𝑉𝑏𝑢𝑠 cos 𝛿𝑠𝑔 + 𝐼𝑠𝑔 sin(𝛿𝑠𝑔 + 𝜑𝑠𝑔 ) (𝑋 ′ 𝑑 + 𝑋𝑙𝑖𝑛𝑒_𝑠𝑔 )

(3.23)

(3.24)

It is noteworthy that unlike inverter-interfaced DG, SG power angle 𝛿𝑠𝑔 is normally not negligible. Based on (3.18)–(3.24), it is possible to calculate the step responses of SG rotor frequency change during a small loading transition, and the results are shown in Fig. 3.9. Note that for the calculation of 𝐵, (3.28) is used instead of (3.20), which is explicated in Section 3.3.3. Parameters of SG are listed in Table 3.2, and parameters of DG are the same as those in Table 3.1. Like the case of single inverter operation, Fig. 3.9 demonstrates that DG with VSG control can contribute more inertia to the system than DG with droop control, since d𝑓/d𝑡 of the former is slower. Also, larger value of 𝐽𝑑𝑔 still increases the inertia of the system. In addition, system with larger 𝐷𝑑𝑔 has slightly smaller oscillation. Similarly, parameters of swing equation have no influence on steady state. - 38 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

(a)

(b) Fig. 3.9 (a) Step responses of SG rotor frequency during a loading transition in the case of parallel operation with a SG with various parameters. (b) Zoom-in of (a).

TABLE 3.2

Parameters of SG

Parameter

Value

Parameter

Value

𝑉𝑏𝑎𝑠𝑒_𝑠𝑔

6.6 kV

𝑋𝑞∗ = 𝑋′𝑞∗

0.770 pu

𝑆𝑏𝑎𝑠𝑒_𝑠𝑔

1 MVA

𝑋′′𝑞∗

0.375 pu

∗ 𝑃0_𝑠𝑔

1 pu

𝑇′′𝑑

0.0348 s

𝜔0

376.99 rad/s

𝑇′′𝑞

0.0346 s

𝑀0∗

8S

𝑇𝑑_𝑠𝑔

0.1 s

∗ 𝑘𝑝_𝑠𝑔

20 pu

𝐼𝑠𝑔

43.1 A

∗ 𝑋𝑙𝑖𝑛𝑒_𝑠𝑔

0.0076 pu

𝜑𝑠𝑔

0.00655 rad

𝑋𝑑∗

1.90 pu

𝑉𝑏𝑢𝑠

6.57 kV

𝑋′∗𝑑

0.314 pu

∆𝑃𝑙𝑜𝑎𝑑

0.0194 MW

𝑋′′𝑑∗

0.280 pu

- 39 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

3.3.3 Effects of Delays in Governor Model and P Droop Controller In the analyses presented in Sections 3.3.1 and 3.3.2, the first-order lag units in the “Governor Model” of VSG and the “P Droop Controller” of droop control are neglected. In this section, effects of these delays are studied. Comparing (3.3) with (3.4), it can be concluded that 𝑘𝑝 should be replaced by 𝑘𝑝 /(1 + 𝑇𝑑 s) for all equations of VSG control if the first-order lag unit is not neglected. However, comparing (3.1) with (3.5), 𝑘𝑝 should be replaced by 𝑘𝑝 (1 + 𝑇𝑑 s) for the equations of droop control. This difference is caused by the inverse of input and output in 𝑃 − 𝜔 droop regulation as it is mentioned in Section 3.2.1. In VSG control, the input is active power and the output is frequency, whereas in droop control, it is the opposite, as illustrated in Figs. 2.5 and 3.2, respectively. If this effect is taken into account for VSG, in the case of single inverter operation, (3.13) should be modified as 𝐷𝑑𝑔 𝐷𝑑𝑔 𝑇𝑑_𝑑𝑔 2 1 + (𝑇𝑑_𝑑𝑔 + )𝑠 + 𝑠 ∆𝜔𝑚_𝑑𝑔 𝐾𝑑𝑔 𝐾𝑑𝑔 =− , ∆𝑃𝑙𝑜𝑎𝑑 𝑘𝑝_𝑑𝑔 + 𝐽𝑑𝑔 𝜔0 𝑠 + 𝐽𝑑𝑔 𝜔0 𝑇𝑑_𝑑𝑔 𝑠 2

(3.25)

and for droop control, (3.14) becomes ∆𝜔𝑚_𝑑𝑔 1 =− . ∆𝑃𝑙𝑜𝑎𝑑 𝑘𝑝_𝑑𝑔 + 𝑇𝑑_𝑑𝑔 𝑘𝑝_𝑑𝑔 s

(3.26)

Meanwhile, in the case of parallel operation with a SG, for VSG and SG, (3.19) and (3.20) should be modified as 𝐴=

∆𝑃𝑜𝑢𝑡_𝑑𝑔 =− ∆𝜔𝑔

𝐵=

𝑘𝑝_𝑑𝑔 + 𝐽𝑑𝑔 𝜔0 𝑠 + 𝑇𝑑_𝑑𝑔 𝐽𝑑𝑔 𝜔0 𝑠 2 , 𝑘𝑝_𝑑𝑔 + 𝐷𝑑𝑔 𝑇𝑑_𝑑𝑔 𝐷𝑑𝑔 + 𝐽𝑑𝑔 𝜔0 2 𝑇𝑑_𝑑𝑔 𝐽𝑑𝑔 𝜔0 3 1 + (𝑇𝑑_𝑑𝑔 + )𝑠 + 𝑠 + 𝑠 𝐾𝑑𝑔 𝐾𝑑𝑔 𝐾𝑑𝑔

(3.27)

𝑘𝑝_𝑠𝑔 + 𝐽𝑠𝑔 𝜔0 𝑠 + 𝑇𝑑_𝑠𝑔 𝐽𝑠𝑔 𝜔0 𝑠 2 , 𝑘𝑝_𝑠𝑔 + 𝐷𝑠𝑔 𝑇𝑑_𝑠𝑔 𝐷𝑠𝑔 + 𝐽𝑠𝑔 𝜔0 2 𝑇𝑑_𝑠𝑔 𝐽𝑠𝑔 𝜔0 3 1 + (𝑇𝑑_𝑠𝑔 + )𝑠 + 𝑠 + 𝑠 𝐾𝑠𝑔 𝐾𝑠𝑔 𝐾𝑠𝑔

(3.28)

∆𝑃𝑜𝑢𝑡_𝑠𝑔 =− ∆𝜔𝑔

respectively, and for droop control, (3.21) becomes 𝐴=

∆𝑃𝑜𝑢𝑡_𝑑𝑔 =− ∆𝜔𝑔

𝑘𝑝_𝑑𝑔 + 𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔 𝑠 . 𝑘𝑝_𝑑𝑔 𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔 2 1+ 𝑠+ 𝑠 𝐾𝑑𝑔 𝐾𝑑𝑔

(3.29)

Based on (3.25)–(3.29), step responses of frequency can be recalculated and then compared with cases without consideration of delays, as shown in Figs. 3.10 and 3.11. The time constant 𝑇𝑑_𝑑𝑔 is assumed to be 0.1 s.

- 40 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.10

Effects of delays on step responses of DG frequency during a loading transition in the case of single inverter operation.

Fig. 3.11

Effects of delays on step responses of SG rotor frequency during a loading transition in the case of parallel operation with a SG.

Figs. 3.10 and 3.11 illustrate the point that inverse of input and output in 𝑃 − 𝜔 droop control law results in different effect of delay for each control method. The delay makes the frequency of systems with VSG control change faster, but makes that of systems with droop control change more slowly in both the case of single inverter operation and the case of parallel operation with a SG. That is to say, the delay has a positive effect on droop control but a negative effect on VSG control.

3.3.4 Inertial Droop Control It is interesting to compare (3.13) with (3.26), and (3.19) with (3.29). If 𝑇𝑑_𝑑𝑔 is increased up to 𝑇𝑑_𝑑𝑔 =

𝐽𝑑𝑔 𝜔0 , 𝑘𝑝_𝑑𝑔

(3.30)

the only difference between (3.13) and (3.26), or (3.19) and (3.29) is that the equations of VSG control have terms coming from 𝐷𝑑𝑔 , whereas those of droop control do not. That is to say, by adding a first-order lag unit, with time constant 𝑇𝑑_𝑑𝑔 specified by (3.30), into P droop controller, droop control can imitate the performance of VSG with a moment of inertia equal to 𝐽𝑑𝑔 . - 41 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control Furthermore, if a first-order lead unit with a time constant 𝑇𝑎_𝑑𝑔 is also added into P droop controller, as shown in Fig. 3.12, (3.26) and (3.29) become ∆𝜔𝑚_𝑑𝑔 1 + 𝑇𝑎_𝑑𝑔 𝑠 =− , ∆𝑃𝑙𝑜𝑎𝑑 𝑘𝑝_𝑑𝑔 + 𝑇𝑑_𝑑𝑔 𝑘𝑝_𝑑𝑔 s

𝐴=

∆𝑃𝑜𝑢𝑡_𝑑𝑔 =− ∆𝜔𝑔

𝑘𝑝_𝑑𝑔 + 𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔 𝑠 , 𝑘𝑝_𝑑𝑔 𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔 2 1+( + 𝑇𝑎_𝑑𝑔 )𝑠 + 𝑠 𝐾𝑑𝑔 𝐾𝑑𝑔

(3.31)

(3.32)

respectively. If the time constant 𝑇𝑎_𝑑𝑔 is set to

Fig. 3.12

P droop controller of droop control with a first-order lead-lag unit.

(a)

(b)

Fig. 3.13

(a) Step responses of SG rotor frequency during a loading transition in the case of

parallel operation with a SG with specified lag or lead-lag unit in droop control. (b) Zoom-in of (a).

- 42 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

𝑇𝑎_𝑑𝑔 =

𝐷𝑑𝑔 , 𝐾𝑑𝑔

(3.33)

then (3.31) is equivalent to (3.13), and (3.32) is equivalent to (3.19). This conclusion is proved by Fig. 3.13. By adding a first-order lag unit with the time constant specified by (3.30), droop control results in similar step response to VSG control, with slightly larger oscillation due to lack of damping factor. Additionally, when a first-order lead unit with the time constant specified by (3.33) is also added, droop control leads to exactly the same step response as VSG control. This implies that during small disturbance, VSG can be approximated by droop control, with a first-order lag unit to simulate inertia, and with a first-order lead unit to simulate damping factor. Although similar conclusion on the relation between first-order lag unit and inertia is mentioned in [3], [4], the relation between first-order lead unit and damping factor has not been discussed in the literature.

3.4 Comparisons of Active Power Oscillation Although VSG control outperforms droop control in the aspect of dynamic frequency performance, it is also known that the swing equation may cause oscillation in output active power during parallel operation. To understand this point, state-space models of the case of parallel operation with a SG are built, for both VSG and droop control, based on small-signal relations developed in Section 3.3. {

𝒙̇ = 𝑨𝒙 + 𝑩𝒘 , 𝒚 = 𝑪𝒙 + 𝑫𝒘

(3.34)

where 𝒘 = [∆𝑃𝑙𝑜𝑎𝑑 ] 𝒚 = [∆𝜔𝑚_𝑠𝑔

∆𝜔𝑚_𝑑𝑔

∆𝑃𝑜𝑢𝑡_𝑠𝑔

(3.35) ∆𝑃𝑜𝑢𝑡_𝑑𝑔 ]𝑇

(3.36)

For VSG control: 𝐷𝑠𝑔 ∆𝑃 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝑙𝑜𝑎𝑑 𝐷𝑑𝑔 ∆𝜔𝑚_𝑑𝑔 + ∆𝑃 𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝑙𝑜𝑎𝑑 𝒙= 1 ∆𝛿𝑠𝑔 − ∆𝑃 𝐾𝑠𝑔 + 𝐾𝑑𝑔 𝑙𝑜𝑎𝑑 ∆𝑃𝑖𝑛_𝑠𝑔 ∆𝑃𝑖𝑛_𝑑𝑔 [ ] ∆𝜔𝑚_𝑠𝑔 +

- 43 -

(3.37)

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

𝐷𝑠𝑔 𝐾𝑑𝑔 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐷𝑑𝑔 𝐾𝑠𝑔 𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐾𝑑𝑔 𝐾𝑠𝑔 + 𝐾𝑑𝑔 𝑘𝑝_𝑠𝑔 − 𝑇𝑑_𝑠𝑔



𝑨=



𝑩=

𝐾𝑠𝑔 𝐽𝑠𝑔 𝜔0 𝐾𝑠𝑔 𝐽𝑑𝑔 𝜔0

1 𝐽𝑠𝑔 𝜔0

0

0

1 𝐽𝑑𝑔 𝜔0

0

0

0



0

0

[



𝐷𝑠𝑔 𝐾𝑑𝑔 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐷𝑑𝑔 𝐾𝑠𝑔 − 𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐾𝑑𝑔 − 𝐾𝑠𝑔 + 𝐾𝑑𝑔



𝐾𝑠𝑔 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 )



0

𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔



0

𝐷𝑠𝑔 𝐷𝑑𝑔 𝐾𝑑𝑔 2

𝐽𝑠𝑔 𝐽𝑑𝑔 𝜔02 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 )

+

1

0

𝑇𝑑_𝑠𝑔 0

(3.38)



1 𝑇𝑑_𝑑𝑔 ]

2 𝐷𝑠𝑔 𝐾𝑑𝑔 2

2 𝜔 2 (𝐾 + 𝐾 ) 𝐽𝑠𝑔 𝑠𝑔 𝑑𝑔 0

2 𝐷𝑑𝑔 𝐾𝑠𝑔 𝐾𝑠𝑔 𝐷𝑠𝑔 𝐷𝑑𝑔 𝐾𝑠𝑔 1 + − + 2 2 2 2 2 𝐽𝑑𝑔 𝜔0 𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐽 𝐽 𝜔 (𝐾 + 𝐾 ) 𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝑠𝑔 𝑑𝑔 0 𝑠𝑔 𝑑𝑔 𝐷𝑠𝑔 𝐾𝑑𝑔 𝐷𝑑𝑔 𝐾𝑑𝑔 − 2+ 2 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝑘𝑝_𝑠𝑔 𝐷𝑠𝑔

(3.39)

𝑇𝑑_𝑠𝑔 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝑘𝑝_𝑑𝑔 𝐷𝑑𝑔 𝑇𝑑_𝑑𝑔 𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 )

[

1 0 𝑪= 0 [0

− −

𝑫=

0 1 0 0

0 0 𝐾𝑠𝑔 −𝐾𝑠𝑔

0 0 0 0

0 0 0 0]

]

(3.40)

𝐷𝑠𝑔 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐷𝑑𝑔

𝐽𝑑𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐾𝑠𝑔 𝐾𝑠𝑔 + 𝐾𝑑𝑔 𝐾𝑑𝑔 𝐾𝑠𝑔 + 𝐾𝑑𝑔 [ ]

(3.41)

For droop control: ∆𝜔𝑚_𝑠𝑔 + 𝒙= [

𝐷𝑠𝑔

∆𝑃𝑙𝑜𝑎𝑑 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) ∆𝜔𝑚_𝑑𝑔 1 ∆𝛿𝑠𝑔 − ∆𝑃 𝐾𝑠𝑔 + 𝐾𝑑𝑔 𝑙𝑜𝑎𝑑 ∆𝑃𝑖𝑛_𝑠𝑔 ]

- 44 -

(3.42)

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control



𝐷𝑠𝑔 𝐾𝑑𝑔

𝐷𝑠𝑔 𝐾𝑑𝑔

𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 )

𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 1 − 𝑇𝑑_𝑑𝑔 𝐾𝑑𝑔 − 𝐾𝑠𝑔 + 𝐾𝑑𝑔

0 𝑨=

[

𝐾𝑑𝑔 𝐾𝑠𝑔 + 𝐾𝑑𝑔 𝑘𝑝_𝑠𝑔 − 𝑇𝑑_𝑠𝑔



𝑩=

[

1 𝐽𝑠𝑔 𝜔0

0

0

0

𝐾𝑠𝑔 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) −

𝐾𝑠𝑔 𝐽𝑠𝑔 𝜔0 𝐾𝑠𝑔 𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔 −

+

0

0 (3.43)



1 𝑇𝑑_𝑠𝑔 ]

2 𝐷𝑠𝑔 𝐾𝑑𝑔 2

2 𝜔 2 (𝐾 + 𝐾 ) 𝐽𝑠𝑔 𝑠𝑔 𝑑𝑔 0 𝐾𝑠𝑔

1 + 𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔 𝑘𝑝_𝑑𝑔 𝑇𝑑_𝑑𝑔 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝐷𝑠𝑔 𝐾𝑑𝑔 − 2 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 𝑘𝑝_𝑠𝑔 𝐷𝑠𝑔 𝑇𝑑_𝑠𝑔 𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 1 0 𝑪= 0 [0



0 1 0 0

0 0 𝐾𝑠𝑔 −𝐾𝑠𝑔

(3.44)

]

0 0 0 0]

(3.45)

𝐷𝑠𝑔

𝐽𝑠𝑔 𝜔0 (𝐾𝑠𝑔 + 𝐾𝑑𝑔 ) 0 𝐾𝑠𝑔 𝑫= 𝐾𝑠𝑔 + 𝐾𝑑𝑔 𝐾𝑑𝑔 𝐾𝑠𝑔 + 𝐾𝑑𝑔 [ ]

(3.46)

It can be proved that the transfer functions of the first output ∆𝜔𝑚_𝑠𝑔 over the input ∆𝑃𝑙𝑜𝑎𝑑 deduced from these state-space models are the same as those described by (3.18), (3.27)–(3.29). Since oscillations in output variables, including DG output power ∆𝑃𝑜𝑢𝑡_𝑑𝑔 , are determined by the eigenvalues of state matrix 𝑨, it is important to analyze how these eigenvalues vary according to different parameters, as shown in Fig. 3.14. In each diagram, radial lines indicate damping ratio 𝜁, whereas circle lines indicate undamped nature frequency 𝜔𝑛 . Parameters used for calculation are the same as those listed in Tables 3.1 and 3.2. It is implied that VSG control is more oscillatory than droop control due to smaller 𝜁 of the complex conjugate eigenvalues. Although oscillation in output power is a common phenomenon in SG, it may cause overcurrent in DG and stop the inverter, because an inverter usually has weaker overload ability than a SG of same rating. However, this problem can be solved by increasing damping factor 𝐷𝑑𝑔 and/or line reactance 𝑋𝑑𝑔 , as 𝜁 of the complex conjugate eigenvalues in- 45 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.14

Eigenvalues when (a) Jdg of VSG varies from 1.5-4J0 to 1.55J0, (b) Ddg of VSG varies from

2-4D0 to 25D0, (c) Xdg of VSG varies from 2.5-4×0.1374 pu to 2.55×0.1374 pu, (d) Td_dg of VSG varies from 1.09-4×0.1 s to 1.095×0.1 s and (e) Td_dg of droop control varies from 1.25-4×0.1 s to 1.255×0.1 s.

creases in these cases as it is shown in Fig. 3.14. For example, a well-designed damping method based on modification of 𝐷𝑑𝑔 and considering line resistance is presented in [37]. As for 𝑋𝑑𝑔 , it can be increased by adjusting the stator impedance using virtual impedance control, which is further discussed in next chapter. In addition, it is shown that 𝐽𝑑𝑔 affects the damped nature frequency 𝜔𝑑 , which is indicated by the distance between the eigenvalues and the real axis, but has barely any effect on the damping ratio.

- 46 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control It is also shown that the increase of 𝑇𝑑_𝑑𝑔 not only results in higher d𝑓/d𝑡 as discussed in last section, but also makes the system more oscillatory. Therefore, it is better not to simulate governor delay in VSG control. Droop control may also become oscillatory if the lag time constant 𝑇𝑑_𝑑𝑔 is very large. In this case, its distribution of eigenvalues becomes similar to that of VSG control. This verifies the conclusion in Section 3.3.4, that droop control can be used to simulate VSG by increasing 𝑇𝑑_𝑑𝑔 . Moreover, for both control methods, no matter how parameters change, no right-half-plan pole is observed. This implies that parameters evaluated in this section do not influence the stability of active power control in the case of parallel operation with a SG.

Fig. 3.15

Fig. 3.16

Fig. 3.17

Simulation circuit of the case of single inverter operation.

Simulation circuit of the case of parallel operation with a SG.

Simulation results for the case of single inverter operation to verify Fig. 3.7.

- 47 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

3.5 Simulation Results To verify the theoretical results, simulations are performed in PSCAD/EMTDC for all cases discussed in Section 3.3. Simulation circuits for the case of single inverter operation and that of parallel operation with a SG are shown in Figs. 3.15 and 3.16, respectively, and the results are shown in Figs. 3.17–3.21. All parameters are the same as those listed in Tables 3.1 and 3.2, except that resistance of

Fig. 3.18

Simulation results for the case of single inverter operation to verify Fig. 3.10.

(a)

(b) Fig. 3.19

Simulation results for the case of parallel operation with a SG to verify Fig. 3.9.

- 48 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.20

Simulation results for the case of parallel operation with a SG to verify Fig. 3.11.

(a)

(b) Fig. 3.21

Simulation results for the case of parallel operation with a SG to verify Fig. 3.13.

transmission lines is taken into account in the simulation, as shown in Figs. 3.15 and 3.16. It should be noticed that for the case of “droop control without delay”, a first-order filter with the time constant set to 0.005 s is applied in simulations (and in experiments discussed in next section), otherwise noises in ∆𝜔𝑚_𝑑𝑔 would be very large. Even with the filter, ripples can still be observed in Figs. 3.17 and 3.19 for this case.

- 49 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

As it can be observed, in all cases, simulation results (solid lines) almost overlap corresponding theoretical results (dotted lines). Therefore, it can be concluded that the small signal models are verified. By comparing the rate of change of frequency and the amplitude of oscillations of each simulation results, same conclusions can be made as in Section 3.3. Furthermore, for the case of parallel operation with a SG (Figs. 3.19–3.21), simulation results are slightly delayed compared with theoretical results, probably because in simulation, the input disturbance ∆𝑃𝑙𝑜𝑎𝑑 , which is realized by switching on additional load, is not an ideal step due to the existence of line reactance. It can also be noted that the amplitude of oscillations in simulation results are smaller than that in theoretical results, probably because simulation circuits include line resistance, which provides additional damping for the system. In Fig 3.21, there is still slight difference between the simulation result of droop control with specified lead-lag unit (c1) and that of VSG (d1), whereas in theoretical results, the two results should be equivalent as shown by line (c2) and line (d2). This is probably due to the presence of line resistance as mentioned above. However, the damping effect of the first-order lead unit is confirmed by comparing line (b1) with line (c1).

3.6 Experimental Results Scale-down experiments are also executed to support the points in Section 3.3. Experimental circuits of the case of single inverter operation and that of parallel operation with a SG are shown in Figs. 3.22 and 3.23, respectively. The setup of experiment system is shown in Figs. 3.24–3.26.

Fig. 3.22

Fig. 3.23

Experimental circuit of the case of single inverter operation.

Experimental circuit of the case of parallel operation with a SG.

- 50 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.24

Fig. 3.25

Photo of Inverters and DSP controllers.

Photo of synchronous generator moved by a dc motor.

- 51 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.26

TABLE 3.3

Photos of the load systems.

Experimental Parameters for the Case of Single Inverter Operation

Parameter

Value

Parameter

Value

𝐸𝑑𝑔

207 V

𝐽0

0.2815 kg∙m2

𝑆𝑏𝑎𝑠𝑒_𝑑𝑔

5 kVA

𝐷0∗

17 pu

𝑃0_𝑑𝑔

1 pu

𝛿𝑑𝑔

0

𝜔0

376.99 rad/s

𝑉𝑏𝑢𝑠

447.05 V

∗ 𝑘𝑝_𝑑𝑔

20 pu

∆𝑃𝑙𝑜𝑎𝑑

0.34 kW

TABLE 3.4

Experimental Parameters for the Case of Parallel Operation with a SG

Parameter

Value

Parameter

Value

𝑉𝑏𝑎𝑠𝑒_𝑠𝑔

230 V

𝑋𝑞

1.31 pu

𝑆𝑏𝑎𝑠𝑒_𝑠𝑔

10 kVA

𝑋′𝑞

0.55 pu

𝑃0_𝑠𝑔 = 𝑃0_𝑑𝑔

0 pu

𝑋′′𝑞

0.27 pu

𝜔0

376.99 rad/s

𝑇′′𝑑

0.01 s

𝐽𝑠𝑔

0.563 kg∙m2

𝑇′′𝑞

0.02 s

∗ 𝑘𝑝_𝑠𝑔

20 pu

𝐼𝑠𝑔

4.77 A

𝑋𝑑

1.35 pu

𝜑𝑠𝑔

0.76 rad

𝑋′𝑑

0.48 pu

𝑉𝑏𝑢𝑠

454.8 V

𝑋′′𝑑

0.27 pu

∆𝑃𝑙𝑜𝑎𝑑

1.29 kW

Other DG parameters are the same as those in Table 3.3

- 52 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.27

Fig. 3.28

Transmission Unit (TU).

Photo of Transmission Units.

Three-phase power supply rectified by a diode bridge is used to imitate the dc output of a DG. The block “transmission unit (TU)” in these graphs is a Π circuit to simulate a section of 40 km HV transmission line, which is illustrated in Fig. 3.27 and its photo is shown in Fig. 3.28. Parameters of the case of single inverter operation and that of parallel operation with a SG are listed in Tables 3.3 and 3.4, respectively, and the results are shown in Figs. 3.29–3.33. For the case of single inverter operation, experimental results (solid lines) coincide with corresponding theoretical results (dotted lines). This proves again that the small-signal models and the conclusions discussed in Section 3.3 are correct. For the case of parallel operation with a SG, by comparing each case of experimental results, the same conclusions can be drawn as those in Section 3.3. In Fig. 3.31, system with VSG control still results in slower frequency change than that with droop control, and the frequency changes faster when 𝐽𝑑𝑔 decreases. In Fig. 3.32 it can still be noticed that the delay (𝑇𝑑_𝑑𝑔 = 0.1 s) makes the fre- 53 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.29

Fig. 3.30

Experimental results for the case of single inverter operation to verify effects of parameters.

Experimental results for the case of single inverter operation to verify effects of delays.

quency change faster in VSG control, but makes the frequency change more slowly in droop control. Similarly, in Fig. 3.33, with specified lag unit or lead-lag unit, droop control has similar dynamic response to VSG. Although in experimental results, it is difficult to confirm the difference in amplitude of oscillations due to noises and insufficient measurement resolution, simulation results are enough to confirm author’s points.

3.7 Conclusion In this chapter, small-signal models of VSG control and of droop control were built, for both cases of single inverter operation and parallel operation with a SG, to compare the dynamic responses of the two control methods. All results were verified by simulations and experiments. Oscillation phenomena were studied through state-space models. Results are summarized as follows. (1)

It was demonstrated that VSG has larger inertia than droop control and therefore better frequency stability, and the amount of inertia depends on virtual moment of inertia 𝐽 whereas the damping ratio depends on damping factor 𝐷 and output reactance 𝑋. It was also proved - 54 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

Fig. 3.31

Experimental results for the case of parallel operation with a SG to verify effects of parameters.

Fig. 3.32

Experimental results for the case of parallel operation with a SG to verify effects of delays.

Fig. 3.33

Experimental results for the case of parallel operation with a SG to verify inertial droop control.

that the delay in governor of VSG reduces the inertia and amplifies oscillation. As a result, it is recommended to remove governor delay from VSG control. Contrarily, delay in P droop controller of droop control can increase the inertia. (2)

It was shown that droop control with a well-designed first-order lead-lag unit in P droop controller has equivalent small-signal model to that of VSG control. This modified droop control, which can be called inertial droop control, provides a novel solution of virtual inertia, which is more familiar to engineers working on UPS and microgrid applications.

(3)

It was also pointed out that the output active power of VSG is more oscillatory than that of droop control, but this problem can be solved by tuning the damping factor and/or the output - 55 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

reactance. Besides, it was proved that active power controls of both VSG control and droop control are stable. (4)

It was shown that VSG control and the proposed inertial droop control inherit the advantages of droop control, and in addition, provides inertia support for the system. This implies that in the applications where inertia is an important index, e.g. in microgrids, VSG control and the proposed inertial droop control have the potential to replace conventional inertia-less droop control.

(5)

The small-signal models and state-space models presented in this chapter provide novel analytical approaches for understanding the dynamic characteristics of VSG and droop control, which may stimulate new ideas on improving dynamic performances of both control methods, e.g. the method to improve transient active power performance of parallel inverters presented in next chapter.

References [1]

J. Liu, Y. Miura, and T. Ise, “Dynamic characteristics and stability comparisons between virtual synchronous generator and droop control in inverter-based distributed generators,” in Proc. Int. Power Electron. Conf. (IPEC-Hiroshima ECCE-Asia), 2014, pp. 1536–1543.

[2]

J. Liu, Y. Miura, and T. Ise, “Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter-based distributed generators,” IEEE Trans. Power Electron., vol. 31, no. 5, pp. 3600–3611, May 2016.

[3]

M. Guan, W. Pan, J. Zhang, Q. Hao, J. Cheng, and X. Zheng, “Synchronous generator emulation control strategy for voltage source converter (VSC) stations,” IEEE Trans. Power Syst., vol. 30, no. 6, pp. 3093–3101, Nov. 2015.

[4]

Y. Du, J. M. Guerrero, L. Chang, J. Su, and M. Mao, “Modeling, analysis, and design of a frequency-droop-based virtual synchronous generator for microgrid applications,” in Proc. IEEE ECCE Asia Downunder, 2013, pp. 643–649.

[5]

M. C. Chandorkar, D. M. Divan, and R. Adapa, “Control of parallel connected inverters in standalone ac supply systems,” IEEE Trans. Ind. Appl., vol. 29, no. 1, pp. 136–143, Jan./Feb. 1993.

[6]

K. Debrabandere, B. Bolsens, J. Van den Keybus, A.Woyte, J. Driesen, and R. Belmans, “A voltage and frequency droop control method for parallel inverters,” IEEE Trans. Power Electron., vol. 22, no. 4, pp. 1107–1115, Jul. 2007.

[7]

H. Nikkhajoei and R. H. Lasseter, “Distributed generation interface to the CERTS microgrid,” IEEE Trans. Power Del., vol. 24, no. 3, pp. 1598–1608, Jul. 2009.

[8]

A. Engler and N. Soultanis, “Droop control in LV-grids,” in Proc. Int. Conf. Future Power Syst., 2005, pp. 1–6.

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Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control

[9]

J. M. Guerrero, J. Matas, L. G. De Vicuña, M. Castilla, and J. Miret, “Decentralized control for parallel operation of distributed generation inverters using resistive output impedance,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 994–1004, Apr. 2007.

[10] T. L. Vandoorn, B. Meersman, L. Degroote, B. Renders, and L. Vandevelde, “A control strategy for islanded microgrids with dc-link voltage control,” IEEE Trans. Power Del., vol. 26, no. 2, pp. 703–713, Apr. 2011. [11] T. L. Vandoorn, B. Meersman, J. D. M. De Kooning, and L. Vandevelde, “Analogy between conventional grid control and islanded microgrid control based on a global DC-link voltage droop,” IEEE Trans. Power Del., vol. 27, no. 3, pp. 1405–1414, Jul. 2012. [12] Y. Li and Y. W. Li, “Power management of inverter interfaced autonomous microgrid based on virtual frequency-voltage frame,” IEEE Trans. Smart Grid, vol. 2, no.1, pp. 30–40, Mar. 2011. [13] J. A. Peças Lopes, C. L. Moreira, and A. G. Madureira, “Defining control strategies for MicroGrids islanded operation,”,” IEEE Trans. Power Syst., vol. 21, no. 2, pp. 916–924, May 2006. [14] J. C Vasquez, J. M. Guerrero, M. Savaghebi, J. Eloy-Garcia, and R. Teodorescu, “Modeling, analysis, and design of stationary-reference-frame droop-controlled parallel three-phase voltage source inverters,” IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1271–1280, Apr. 2013. [15] J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. De Vicuña, and M. Castilla, “Hierarchical control of droop-controlled DC and AC microgrids—A general approach towards standardization,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 158–172, Jan. 2011. [16] A. Bidram and A. Davoudi, “Hierarchical structure of microgrids control system,” IEEE Trans. Smart Grid, vol. 3, no. 4, pp. 1963–1976, Dec. 2012. [17] Q. Shafiee, J. M. Guerrero, and J. C. Vasquez, “Distributed secondary control for islanded microgrids — a novel approach,” IEEE Trans. Power Electron., vol. 29, no. 2, pp. 1018–1031, Feb. 2014. [18] A. Micallef, M. Apap, C. Spiteri-Staines, J. M. Guerrero, and J. C. Vasquez, “Reactive power sharing and voltage harmonic distortion compensation of droop controlled single phase islanded microgrids,” IEEE Trans. Smart Grid, vol. 5, no. 3, pp. 1149–1158, May 2014. [19] J. He and Y. W. Li, “An enhanced microgrid load demand sharing strategy,” IEEE Trans. Power Electron., vol. 27, no. 9, pp. 3984–3995, Sept. 2012. [20] J. He, Y. W. Li, and F. Blaabjerg, “An enhanced islanding microgrid reactive power, imbalance power, and harmonic power sharing scheme,” IEEE Trans. Power Electron., vol. 30, no. 6, pp. 3389–3401, Jun. 2015. [21] H. Mahmood, D. Michaelson, and J. Jiang, “Accurate reactive power sharing in an islanded microgrid using adaptive virtual impedances,” IEEE Trans. Power Electron., vol. 30, no. 3, pp. 1605–1617, Mar. 2015. - 57 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control [22] H. Han, Y. Liu, Y. Sun, M. Su, and J. M. Guerrero, “An improved droop control strategy for reactive power sharing in islanded microgrid,” IEEE Trans. Power Electron., vol. 30, no. 6, pp. 3133–3141, Jun. 2015. [23] J. He, Y. W. Li, J. M. Guerrero, F. Blaabjerg, and J. C. Vasquez, “An islanding microgrid power sharing approach using enhanced virtual impedance control scheme,” IEEE Trans. Power Electron., vol. 28, no. 11, pp. 5272–5282, Nov. 2013. [24] Y. W. Li and C.-N. Kao, “An accurate power control strategy for power-electronics-interfaced distributed generation units operating in a low-voltage multibus microgrid,” IEEE Trans. Power Electron., vol. 24, no. 12, pp. 2977–2988, Dec. 2009. [25] W. Yao, M. Chen, J. M. Guerrero, and Z.-M. Qian, “Design and analysis of the droop control method for parallel inverters considering the impact of the complex impedance on the power sharing,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 576–588, Feb. 2011. [26] Q.-C. Zhong, “Robust droop controller for accurate proportional load sharing among inverters operated in parallel,” IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1281–1290, Apr. 2013. [27] C-.T. Lee, C-.C. Chu, and P-.T. Cheng, “A new droop control method for the autonomous operation of distributed energy resource interface converters,” IEEE Trans. Power Electron., vol. 28, no. 4, pp. 1980–1993, Apr. 2013. [28] Y. Zhu, Z. Fang, F. Wang, B. Liu, and Y. Zhao, “A wireless load sharing strategy for islanded microgrid based on feeder current sensing,” IEEE Trans. Power Electron., vol. 30, no. 12, pp.6706–6719, Dec. 2015. [29] M. B. Delghavi and A. Yazdani, “Islanded-mode control of electronically coupled distributed-resource units under unbalanced and nonlinear load conditions,” IEEE Trans. Power Del., vol. 26, no. 2, pp. 661–673, Apr. 2011. [30] T.-L. Lee and P.-T. Cheng, “Design of a new cooperative harmonic filtering strategy for distributed generation interface converters in an islanding network,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1919–1927, Sept. 2007. [31] J. Hu, J. Zhu, D.G. Dorrell, and J. M. Guerrero, “Virtual flux droop method — a new control strategy of inverters in microgrids,” IEEE Trans. Power Electron., vol. 29, no. 9, pp. 4704– 4711, Sept. 2014. [32] I.-Y. Chung, W. Liu, D. A. Cartes,, E. G. Jr. Collins, and S.-I. Moon, “Control methods of inverter-interfaced distributed generators in a microgrid system,” IEEE Trans. Ind. Appl., vol. 46, no. 3, pp. 1078–1088, May/Jun. 2010. [33] R. Majumder, B. Chaudhuri, A. Ghosh, R. Majumder, G. Ledwich, and F. Zare, “Improvement of stability and load sharing in an autonomous microgrid using supplementary droop control loop,” IEEE Trans. Power Syst., vol. 25, no. 2, pp. 796–808, May 2010. [34] J. M. Guerrero, L. G. De Vicuña, J. Matas, M. Castilla, and J. Miret, “Output impedance design of parallel-connected UPS inverters with wireless load-sharing control,” IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1126–1135, Aug. 2005. - 58 -

Chapter 3 Dynamic Characteristics Comparisons Between Droop Control and VSG Control [35] J. M. Guerrero, L. Hang, and J. Uceda, “Control of distributed uninterruptible power supply systems,” IEEE Trans. Ind. Electron., vol. 55, no. 8, pp. 2845–2859, Aug. 2008. [36] J. Machowski, J. Bialek, and J. R. Bumby, Power System Dynamics and Stability. New York: John Wiley & Sons, 1997, pp. 141–182. [37] T. Shintai, Y. Miura, and T. Ise, “Oscillation damping of a distributed generator using a virtual synchronous generator,” IEEE Trans. Power Del., vol. 29, no. 2, pp. 668–676, Apr. 2014.

- 59 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids 4.1 Introduction In this chapter, the application of VSG control in a microgrid composed of parallel inverter-interfaced DGs is discussed [1]. As it is discussed in Chapter 3, VSG control can be considered as a potential upgrade for the communication-less control method of a microgrid thanks to its inertia support feature. However, when VSG control is applied in microgrids, several problems have been noticed, such as oscillation in active power during a disturbance, inappropriate transient active power sharing during loading transition and errors in reactive power sharing. Active power oscillation during a disturbance is introduced by the well-known feature of the swing equation, thus it is an inherent feature for a real SG as well as a VSG. It is not a critical problem for SGs because they usually have considerable overload capabilities, but the overload capabilities of inverter-interfaced DGs are not high enough to ride though a large oscillation. However, this oscillation can be damped by properly increasing the damping ratio [2] or using alternating moment of inertia [3]. Using smaller inertia may also lead to reduced oscillation [4]; however, it is not encouraged because providing a large amount of virtual inertia is an advantage that distinguishes VSG control from other control methods. In this chapter, a novel method for oscillation damping is proposed based on increasing the virtual stator reactance. Due to the oscillatory feature of VSG, inappropriate transient active power sharing during loading transition may also cause oscillation, which is avoidable if the swing equation and output impedance are designed properly, as it is analyzed in this chapter. This inappropriate transient active power sharing is also reported in [5]; however, proper solution is not proposed. Sharing transient loads between SG and DG is addressed in [6]; however, theoretical analysis is not provided. The inaccurate reactive power sharing is a well-known problem in conventional 𝑄 − 𝑉 droop control, and the same problem is reported in active power sharing of 𝑃 − 𝑉 droop control. In 𝑄 − 𝑉 or 𝑃 − 𝑉 droop control, output voltage is regulated according to reactive/active power sharing, but the output voltage of each DG is not equal due to unequal line voltage drop. This problem has received considerable attention in the literature, and many control strategies are proposed to address this issue [7]–[23]. A comprehensive solution is to eliminate the mismatch of DG output impedance [7], [8]; however, this method cannot guarantee accurate reactive power sharing if active power is not shared according to the power rating ratio. An approach based on line voltage drop compensation is proposed in [9]. However, a grid-connected mode operation is required for the - 60 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

evaluation of line parameters, which is not feasible for an isolated microgrid. Other communication-less approaches, e.g. 𝑄– d𝑉/d𝑡 droop control [10], adaptive voltage droop [11], and virtual capacitor control [12] are also proposed. However, the reactive power sharing errors cannot be completely eliminated by these methods, as it is demonstrated in respective experimental results. In some approaches, communication is used to improve reactive power sharing accuracy, such as secondary control signals from MGCC [13]–[18], master-slave communication [19], and communication between DGs [20]. However, as accurate reactive power sharing is a basic function of a microgrid, it is always preferred to solve this problem in a communication-less manner considering the probable communication fault. In this chapter, a communication-less approach is proposed based on the inversed voltage droop (𝑉 − 𝑄 droop) feature of VSG control and common ac bus voltage estimation. By applying the proposed method, reactive power sharing is immune to line impedance mismatch and active power sharing change. The idea to use ac bus voltage as a common reference shares some similarities with the approaches presented in [21]–[23]. However, in these works, measured bus voltage is used directly, whereas it may not be feasible in microgrid applications if DGs are not installed in the proximity of the ac bus. In this chapter, bus voltage is estimated based on the available local measurement, thus there should be no installation difficulty in field applications. The rest of this chapter is organized as follows. In Section 4.2, a state-space model of islanded microgrid using VSG control is built, and the principle of the proposed oscillation damping method is derived from eigenvalue analysis of this model. Proper parameter design for appropriate transient load sharing based on poles-zeros cancellation is also discussed based on the same model. In Section 4.3, the cause of reactive power sharing errors is discussed and a novel accurate reactive power sharing method is proposed. The enhanced VSG control strategy based on aforementioned discussion is presented in Section 4.4. Simulation and experiment results are shown in Sections 4.5 and 4.6, respectively. Finally, conclusions are given in Section 4.7.

4.2 Analyses of Transient Active Power Performance 4.2.1 Closed-Loop State-Space Model In this chapter, an islanded microgrid which consists of two DGs using VSG control is studied, as it is shown in Fig. 4.1. The DGs are connected to a common ac bus via distribution lines, to supply the loads inside the microgrid. Note that the capacitor of the DG output LC filter in Fig. 2.2 is neglected, as its susceptance is usually negligible at fundamental frequency. In order to understand the causes of active power oscillation and to find proper solutions, a state-space model for the closed-loop active power control of the microgrid shown in Fig. 4.1 can be obtained as given in (4.1)–(4.8) with a deduction process same as that shown in Section 3.4. As it is concluded that the governor delay should be removed in Chapter 3, the governor first-order lag unit

- 61 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

Fig. 4.1

Structure of a microgrid composed of two DGs in islanded mode.

is removed by setting 𝑇𝑑 = 0 in this chapter. Therefore, the rank of the state-space model is reduced to 3 as shown in the following equations. {

𝒙̇ = 𝑨𝒙 + 𝑩𝒘 , 𝒚 = 𝑪𝒙 + 𝑫𝒘

(4.1)

∆𝑃0_1

(4.2)

where 𝒘 = [∆𝑃𝑙𝑜𝑎𝑑 𝒚 = [∆𝜔𝑚1

∆𝜔𝑚2

∆𝑃0_2 ]𝑇

∆𝑃𝑜𝑢𝑡1

∆𝑃𝑜𝑢𝑡2 ]𝑇

(4.3)

𝐷1 ∆𝑃 𝐽1 𝜔0 (𝐾1 + 𝐾2 ) 𝑙𝑜𝑎𝑑 𝐷2 ∆𝑃 𝒙 = ∆𝜔𝑚2 + 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝑙𝑜𝑎𝑑 1 ∆𝛿1 − ∆𝑃 [ ] 𝐾1 + 𝐾2 𝑙𝑜𝑎𝑑 ∆𝜔𝑚1 +

𝑘𝑝1 𝐷1 𝐾2 − 𝐽1 𝜔0 (𝐾1 + 𝐾2 ) 𝐽1 𝜔0 𝐷2 𝐾1 𝑨= 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝐾2 [ 𝐾1 + 𝐾2 −

𝐷1 𝐾2 𝐽1 𝜔0 (𝐾1 + 𝐾2 ) 𝑘𝑝2 𝐷2 𝐾1 − − 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝐽2 𝜔0 𝐾2 − 𝐾1 + 𝐾2

(4.4)

𝐾1 𝐽1 𝜔0 𝐾1 𝐽2 𝜔0



0

(4.5) ]

𝑩 𝐷1 𝑘𝑝1 𝐾1 𝐷1 𝐷2 𝐾2 𝐷12 𝐾2 1 − + + 2 2 2 𝐽1 𝜔0 (𝐾1 + 𝐾2 ) 𝐽1 𝐽2 𝜔0 (𝐾1 + 𝐾2 )2 𝐽1 𝜔0 (𝐾1 + 𝐾2 )2 𝐽12 𝜔02 (𝐾1 + 𝐾2 ) 𝐽1 𝜔0 𝐷2 𝑘𝑝2 1 𝐾1 𝐷1 𝐷2 𝐾1 𝐷22 𝐾1 = − + − + 2 2 + 2 2 0 2 2 2 𝐽2 𝜔0 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝐽1 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝐷1 𝐾2 𝐷2 𝐾2 − + 0 [ 𝐽1 𝜔0 (𝐾1 + 𝐾2 )2 𝐽2 𝜔0 (𝐾1 + 𝐾2 )2 −

- 62 -

0 1 𝐽2 𝜔0 0

(4.6)

]

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

1 0 𝑪=[ 0 0

0 1 0 0

0 0 ] 𝐾1 −𝐾1

𝐷1 𝐽1 𝜔0 (𝐾1 + 𝐾2 ) 𝐷2 − 𝐽2 𝜔0 (𝐾1 + 𝐾2 ) 𝑫= 𝐾1 𝐾1 + 𝐾2 𝐾2 [ 𝐾1 + 𝐾2 −

(4.7)

0

0

0

0

0

0

0

0

(4.8)

]

where subscript 𝑖 = 1,2 indicates the 𝑖 th DG. Here, 𝐾𝑖 = (𝐸𝑖 𝑉𝑏𝑢𝑠 cos𝛿𝑖 )/𝑋𝑖 , and 𝑋𝑖 ≈ 𝑋𝑓 𝑖 + 𝑋𝑙𝑖𝑛𝑒 𝑖 , as it is discussed in Section 3.3.1. Analyses of transient active power control performance in the following parts of present section are based on this model, as it describes the transient performance of variables in 𝒚 after a given disturbance 𝒘.

4.2.2 Oscillation Damping It is a known conclusion in the control theory that the poles of transfer function of 𝑌𝑗 (𝑠)/𝑊𝑘 (𝑠) are available in the eigenvalues of 𝑨, for any 𝑗, 𝑘 Therefore, the studies on eigenvalues of 𝑨 should give some clues to damping methods for oscillations in ∆𝑃𝑜𝑢𝑡 𝑖 . The loci of eigenvalues of 𝑨 with a variation of 𝐷1 or 𝑋1 are shown in Fig. 4.2. Nominal parameters for the eigenvalue loci plots are listed in Table 4.1. In the eigenvalue loci plots, radial dash lines indicate damping ratio 𝜁, and circle dash lines indicate undamped natural frequency 𝜔𝑛 . As it is shown in Fig. 4.2, damping ratio of the complex-conjugate eigenvalues increases if the damping factor 𝐷𝑖 and/or the output reactance impedance 𝑋𝑖 are increased. It should be pointed out that increasing 𝑋𝑖 causes a decrease in damped natural frequency 𝜔𝑑 , which is indicated by the distance between eigenvalue and the real axis. This may result in longer settling time compared with the method of increasing 𝐷𝑖 . However, the approach of increasing output reactance has other merits as follows. (1)

The state-space model is obtained under the assumption that the output impedance of DGs is inductive, as it is discussed in Section 3.3.1. This assumption is less valid if 𝑋𝑖 is small, especially in a LV microgrid in which line impedances are mainly resistive [24]. If this assumption is not valid, the active power and reactive power control cannot be decoupled correctly and the system may become more oscillatory and even unstable.

(2)

To share transient active power properly, output reactance of each DG should be designed equally in per unit value, as it is discussed in next part of this section. Therefore, the problem

- 63 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

Fig. 4.2

Eigenvalue loci with a variation of

(a) 𝐷1∗ (2−4 × 17 pu ~ 25 × 17 pu) or (b) 𝑋1∗ (2−4 × 0.7 pu ~ 25 × 0.7 pu).

TABLE 4.1

State-Space Model Parameters

Parameter

Value

Parameter

Value

𝑆𝑏𝑎𝑠𝑒1

10 kVA

𝑀𝑖∗

8s

𝑆𝑏𝑎𝑠𝑒2

5 kVA

𝐷𝑖∗

17 pu

𝐸0

200 V

𝑘𝑝∗ 𝑖

20 pu

𝜔0

376.99 rad/s

𝑋𝑖∗

0.7 pu

𝐸𝑖 = 𝑉𝑏𝑢𝑠

200 V

cos𝜃𝑖

≈1

of oscillation and that of transient active power sharing can be solved simultaneously by proper stator reactance design. (3)

Moreover, the influence of output reactance mismatch on transient active power sharing becomes smaller if output reactance of DGs is increased, owing to decreased relative errors.

4.2.3 Transient Active Power Sharing If the disturbance comes from a loading transition, the disturbance vector can be written as 𝒘 = [∆𝑃𝑙𝑜𝑎𝑑

0 0]T . The output vector at 𝑡 = 0+ can be calculated through (4.9). 𝒚(0+ ) = 𝑫𝒘

(4.9)

From (4.9), the transient active power sharing at 𝑡 = 0+ is obtained as ∆𝑃𝑜𝑢𝑡1 (0+ ) =

𝐾1 ∆𝑃 , 𝐾1 + 𝐾2 𝑙𝑜𝑎𝑑

(4.10)

∆𝑃𝑜𝑢𝑡2 (0+ ) =

𝐾2 ∆𝑃 . 𝐾1 + 𝐾2 𝑙𝑜𝑎𝑑

(4.11)

The output vector at steady state can be calculated through (4.12). - 64 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

𝒚(∞) = (𝑫 − 𝑪𝑨−1 𝑩)𝒘

(4.12)

From (4.12), the steady-state active power sharing is obtained as ∆𝑃𝑜𝑢𝑡1 (∞) =

𝑘𝑝1 ∆𝑃 . 𝑘𝑝1 + 𝑘𝑝2 𝑙𝑜𝑎𝑑

(4.13)

∆𝑃𝑜𝑢𝑡2 (∞) =

𝑘𝑝2 ∆𝑃 . 𝑘𝑝1 + 𝑘𝑝2 𝑙𝑜𝑎𝑑

(4.14)

The transient power sharing should be equivalent to the steady-state power sharing, in order to avoid unnecessary transient oscillation. Therefore, 𝑘𝑝1 𝐾1 (𝐸1 𝑉𝑏𝑢𝑠 cos𝛿1 )/𝑋1 = = . 𝑘𝑝2 𝐾2 (𝐸2 𝑉𝑏𝑢𝑠 cos𝛿2 )/𝑋2

(4.15)

Knowing that 𝑘𝑝∗ 𝑖 = (𝑘𝑝 𝑖 𝜔0)/𝑆𝑏𝑎𝑠𝑒 𝑖 , 𝑋𝑖∗ = (𝑋𝑖 𝑆𝑏𝑎𝑠𝑒 𝑖 )/𝐸02 , and supposing 𝐸𝑖 ≈ 𝑉𝑏𝑢𝑠 ≈ 𝐸0 , cos𝛿𝑖 ≈ 1, thus ∗ 𝑋1∗ 𝑘𝑝2 = ∗ . 𝑋2∗ 𝑘𝑝1

(4.16)

As it is mentioned in Section 2.3.2, 𝑘𝑝∗ 𝑖 is designed equally so that the active power is shared according to power ratings of DGs in steady state [25]. Therefore, 𝑋1∗ = 𝑋2∗ .

(4.17)

Equation (4.17) is the condition for appropriate transient power sharing at 𝑡 = 0+. This conclusion can be verified by evaluating the poles and zeros of

ed in Fig. 4.3(a).

∆𝑃𝑜𝑢𝑡1 (𝑠) ∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

and

∆𝑃𝑜𝑢𝑡2 (𝑠) ∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

∆𝑃𝑜𝑢𝑡1 (𝑠) ∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

and

∆𝑃𝑜𝑢𝑡2 (𝑠)

, as it is demonstrat-

∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

can be obtained as the elements 𝐺31 (𝑠) and 𝐺41 (𝑠) of the

matrix 𝑮(𝑠) shown in (4.18), respectively. 𝑮(𝑠) = 𝑪(𝑠𝑰 − 𝑨)−1 𝑩 + 𝑫

Fig. 4.3(a) shows that if (4.17) holds, all poles of

∆𝑃𝑜𝑢𝑡1 (𝑠) ∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

(4.18)

and

∆𝑃𝑜𝑢𝑡2 (𝑠) ∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

are cancelled by zeros,

and if (4.17) does not hold, this cancellation does not happen for the complex-conjugate poles. The cancellation of all poles implies a desirable step change of ∆𝑃𝑜𝑢𝑡1 and ∆𝑃𝑜𝑢𝑡2 directly to their respective steady-state values without any oscillation during a loading transition. However, (4.17) can only guarantee appropriate power sharing at 𝑡 = 0+. The transient state during the first several seconds after 𝑡 = 0+ depends on the swing equation parameters, i.e. moment of inertia and damping factor. As it is shown in Figs. 4.3(b) and 4.3(c), if the inertia constant 𝑀𝑖∗ and the per unit damping ratio 𝐷𝑖∗ are not designed equally, the cancellation of poles and zeros - 65 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

Fig. 4.3

Poles and zeros of

∆𝑃𝑜𝑢𝑡1(𝑠) ∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

in the left column and

∆𝑃𝑜𝑢𝑡2(𝑠) ∆𝑃𝑙𝑜𝑎𝑑 (𝑠)

in the right column

with a variation of (a) 𝑋1∗ (2−4 × 0.7 pu ~ 25 × 0.7 pu) (b) 𝑀1∗ (1.3−4 × 8 s ~ 1.35 × 8 s) or (c) 𝐷1∗ (2−4 × 17 pu ~ 25 × 17 pu).

does not happen, either. That is to say, to obtain ideal transient active power sharing, (4.19) and (4.20) should also be guaranteed. 𝑀1∗ = 𝑀2∗ .

(4.19)

𝐷1∗ = 𝐷2∗ .

(4.20)

- 66 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids Equations (4.19) and (4.20) are not difficult to realize since 𝑀𝑖∗ and 𝐷𝑖∗ are virtual parameters that can be easily changed in the control program. As for (4.17), a control method to adjust stator reactance is presented in Section 4.4.

4.3 Improvement of Reactive Power Sharing Fig. 4.4 shows the principles of 𝜔 − 𝑃 and 𝑉 − 𝑄 droop controls in the “Governor Model” and “Q Droop” blocks shown in Figs. 2.5 and 2.6, for the case of 𝑆𝑏𝑎𝑠𝑒1 : 𝑆𝑏𝑎𝑠𝑒2 = 2: 1. As discussed in Section 2.3.2, 𝑘𝑝∗ , 𝑘𝑞∗ , 𝑃0∗ and 𝑄0∗ are designed equally. Based on the predefined linear droop control laws, the desired power sharing 𝑃𝑖𝑛1 : 𝑃𝑖𝑛2 = 2: 1 can be obtained because the governor input is 𝜔𝑚 , and 𝜔𝑚1 = 𝜔𝑚2 is guaranteed in steady state. Following the same principle, to share the reactive power according to the power rating ratio, an equal voltage reference is required. However, for the 𝑉 − 𝑄 droop in the basic VSG control shown in Fig. 2.6, the voltage reference is the line-to-line RMS value of the inverter output voltage, which may be a different value for each DG even in steady state due to the line voltage drop. As most of previous studies are based on 𝑄 − 𝑉 droop, in which the output voltage 𝑉𝑜𝑢𝑡 𝑖 should be regulated based on measured reactive power 𝑄𝑜𝑢𝑡 𝑖 , the basic idea to address this problem is to equalize 𝑉𝑜𝑢𝑡 𝑖 by equalizing the output impedance [7], [8], or by compensating the line voltage drop [9]. Both methods need great effort in design process and complex computations in DG control programs, whereas the resulted reactive power sharing is still influenced by active power sharing. As the voltage does not need to be controlled directly in a 𝑉 − 𝑄 droop control scheme shown in Fig. 2.2, the reference voltage can be chosen other than inverter output voltage. If the line-to-line RMS value of the common ac bus voltage 𝑉𝑏𝑢𝑠 is used instead of the inverter output voltage 𝑉𝑜𝑢𝑡 𝑖 , equal reactive power reference value 𝑄𝑟𝑒𝑓1 = 𝑄𝑟𝑒𝑓2 can be guaranteed, as it is illustrated in Fig. 4.4. Therefore, accurate reactive power sharing 𝑄𝑜𝑢𝑡1 = 𝑄𝑜𝑢𝑡2 should be obtained through the using of reactive power PI controller. Moreover, unlike the inverter output voltage, the bus voltage is not influenced by line voltage drop, which is determined by both active and reactive power. Therefore, reactive power sharing according to the bus voltage is independent from active power.

Fig. 4.4

Principles of 𝜔 − 𝑃 and 𝑉 − 𝑄 droop control.

- 67 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

In some previous researches [21]–[23], direct bus voltage measurement is suggested. However, in field applications, it is difficult to measure 𝑉𝑏𝑢𝑠 directly, as DGs may be installed far away from the common ac bus, and the utilization of communication is not preferred for reliability reason. Therefore, a bus voltage estimation method using local measurement is proposed in next section.

4.4 The Proposed Enhanced VSG Control Scheme The proposed enhanced VSG control scheme is shown in Fig. 4.5. Compared with the basic VSG control, two major modifications are made, i.e., the stator impedance adjuster and the bus voltage estimator, as shown in Figs. 4.6 and 4.7, respectively. In order to facilitate the algorithm in the stator impedance adjuster and the bus voltage estimator, the measured three-phase output voltage and current are converted to αβ frame. As a result, the calculation in the power meter should be based on αβ-frame components instead of three-phase components. Therefore, (2.6) and (2.7) should be replaced by (4.21) and (4.22). 𝑃𝑜𝑢𝑡 = 𝑣𝑜𝑢𝑡_𝛼 𝑖𝑜𝑢𝑡_𝛼 + 𝑣𝑜𝑢𝑡_𝛽 𝑖𝑜𝑢𝑡_𝛽

(4.21)

𝑄𝑜𝑢𝑡 = −𝑣𝑜𝑢𝑡_𝛼 𝑖𝑜𝑢𝑡_𝛽 + 𝑣𝑜𝑢𝑡_𝛽 𝑖𝑜𝑢𝑡_𝛼

(4.22)

The function of stator impedance adjuster shown in Fig. 4.6 is to adjust the output reactance of the DG freely. It is operating as a virtual impedance controller. The transformation from ρθ frame to αβ frame and the inverse transformation used in Fig. 4.6 and the following part of this dissertation are defined in (4.23) and (4.24).

Fig. 4.5

Block diagram of the proposed enhanced VSG control.

- 68 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

Fig. 4.6

Block diagram of the “Stator Impedance Adjuster” block of the enhanced VSG control.

Fig. 4.7

Block diagram of the “Vbus Estimator” block of the enhanced VSG control.

𝛼 𝜌 cos 𝜃 [𝛽 ] = [ ] 𝜌 sin 𝜃

(4.23)

√𝛼 2 + 𝛽 2 𝜌 [ ]=[ 𝛽 ] 𝜃 tan−1 𝛼

(4.24)

The virtual stator inductor is realized by multiplying output current by the virtual stator inductor 𝐿𝑙𝑠 in αβ frame. It will be more accuracy if inductor current through 𝐿𝑓 is used. However, this will increase the number of current sensors, which is not necessary. As the current flowing into 𝐶𝑓 at fundamental frequency is less than few percent of the inductor current, using output current instead of inductor current does not affect the performance of the control scheme. Based on the given analyses in Section 4.2, tuning method of virtual stator inductor 𝐿𝑙𝑠 is suggested to set total output reactance 𝑋𝑖∗ for both DGs in same large per unit value, as shown in (4.25). This approach increases active power damping ratio and shares transient load without oscillation. The target value is proposed to be 0.7 pu because it is a typical value for the total direct-axis transient reactance 𝑋′𝑑 of a real SG. 𝑋𝑖∗ = 𝑆𝑏𝑎𝑠𝑒 𝑖 𝜔𝑚 𝑖 (𝐿𝑙𝑠 𝑖 + 𝐿𝑓 𝑖 + 𝐿𝑙𝑖𝑛𝑒 𝑖 )/𝐸02 = 0.7 pu

(4.25)

The 𝐿𝑓 𝑖 and 𝑍𝑙𝑖𝑛𝑒 𝑖 (𝑅𝑙𝑖𝑛𝑒 𝑖 + 𝑗𝐿𝑙𝑖𝑛𝑒 𝑖 ) are considered as known parameters in this paper. As the scale of microgrid is usually small, the line distance is easily to be measured or fed by the planner. - 69 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids Even if it is not the case, several online measurement or intelligent tuning methods for 𝑍𝑙𝑖𝑛𝑒 𝑖 are available in [24] and [26]. With the proposed design of stator impedance adjustment, oscillation in a VSG-control-based microgrid should be almost eliminated during a loading transition in islanded mode. Particularly, transition from grid-connected mode to islanded mode can also be considered as a loading transition; therefore, the oscillation during an islanding event should also be eliminated with the proposed control strategy, as it is proved by simulation results in next section. As for other disturbances in islanded mode during which the power sharing ratio is changed, e.g. change of active power set value of DG(s), connection/disconnection of DG(s), etc., oscillation cannot be completely eliminated with the proposed solution, but can still be damped owing to the increased total output reactance. The principle of the bus voltage estimator shown in Fig. 4.7 is similar to that of the stator impedance adjuster shown in Fig. 4.6. By calculating the line voltage drop in αβ frame using measured output current and line impedance data, the bus voltage can be estimated from the difference of output voltage and calculated line voltage drop. Since the line-to-line RMS value of estimated bus voltage 𝑉̂𝑏𝑢𝑠 for each DG should be approximately equal, as it is discussed in last section, accurate reactive power sharing can be obtained by using estimated bus voltages as the input references of “Q Droop” instead of respective output voltages of DGs. Although the principle of presented bus voltage estimator is not new, the idea of using this estimator to realize communication-less accurate reactive power sharing can be considered as a contribution in the present work. The modified Q droop controller is shown in Fig 4.8 and can be expressed as 𝑄𝑟𝑒𝑓 = 𝑄0 − 𝑘𝑞 (𝑉̂𝑏𝑢𝑠 − 𝐸0 ).

(4.26)

However, if there is an estimation error in 𝑉̂𝑏𝑢𝑠 , it will cause a reactive power sharing error. ∗ ∗ ∗ ∗ Supposing 𝑉̂𝑏𝑢𝑠1 = 𝑉𝑏𝑢𝑠 + ∆𝑉̂1∗ and 𝑉̂𝑏𝑢𝑠2 = 𝑉𝑏𝑢𝑠 + ∆𝑉̂2∗, substitute them into (4.26), ∗ ∗ 𝑄𝑟𝑒𝑓1 − 𝑄𝑟𝑒𝑓2 = −𝑘𝑞∗ (∆𝑉̂1∗ − ∆𝑉̂2∗ ).

(4.27)

∗ ∗ In steady state, as 𝑄𝑟𝑒𝑓 𝑖 = 𝑄𝑜𝑢𝑡 𝑖 , ∗ ∗ 𝑄𝑜𝑢𝑡1 − 𝑄𝑜𝑢𝑡2 = −𝑘𝑞∗ (∆𝑉̂1∗ − ∆𝑉̂2∗ ).

(4.28)

That is to say, the reactive power sharing error caused by estimation errors is determined by the V-Q droop gain 𝑘𝑞∗ . The design of 𝑘𝑞∗ is a well-known trade-off between voltage deviation and reactive power control accuracy. Considering the probable ripples in the measured RMS value of 𝑉̂𝑏𝑢𝑠 , 𝑘𝑞∗ is recommended to be 5 pu for the present example.

Fig. 4.8

Block diagram of the “Q Droop” block of enhanced VSG control.

- 70 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

It should be pointed out that the increased output reactance by adding the virtual stator inductor 𝐿𝑙𝑠 causes a decrease in the reactive control plant gain. From (3.7), 𝑄𝑜𝑢𝑡 𝑖 =

𝐸𝑖 (𝐸𝑖 − 𝑉𝑏𝑢𝑠 cos𝛿𝑖 ) . 𝑋𝑖

(4.29)

The small-signal model of (4.29) is ∆𝑄𝑜𝑢𝑡 𝑖 =

(𝐸𝑖 − 𝑉𝑏𝑢𝑠 cos𝛿𝑖 )∆𝐸𝑖 + 𝐸𝑖 (∆𝐸𝑖 − ∆𝑉𝑏𝑢𝑠 cos𝛿𝑖 ) . 𝑋𝑖

(4.30)

As cos𝛿𝑖 ≈ 1, 𝐸𝑖 ≈ 𝑉𝑏𝑢𝑠 ≈ 𝐸0, (4.30) can be simplified as ∆𝑄𝑜𝑢𝑡 𝑖 =

Fig. 4.9

𝐸0 (∆𝐸𝑖 − ∆𝑉𝑏𝑢𝑠 ) . 𝑋𝑖

Small-signal model of reactive power control loop.

Fig. 4.10

Bode plot of reactive power control loop.

- 71 -

(4.31)

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

With (4.31), the small-signal model of the reactive power control part can be illustrated as Fig. 4.9. Therefore, in the enhanced VSG control where 𝑋𝑖 is largely increased, in order to keep the bandwidth of the reactive power control loop to be 20 Hz, the gain of PI controller should be increased to compensate the decreased plant gain, as illustrated in Fig. 4.10. The parameters used to plot Fig. 4.10 are related to DG1, which are shown in Fig. 4.11 and Table 4.2. The 20Hz bandwidth is relatively low compared with control methods working on instantaneous value; however, it is fast enough to track the reactive power and regulate the output voltage as it is demonstrated in the simulation and experimental results.

4.5 Simulation Results Simulations are executed in PSCAD/EMTDC environment to verify the effectiveness of the pro-

Fig. 4.11

TABLE 4.2

Simulation circuit.

Simulation Parameters

Common Parameters Parameter

Value

Parameter

Value

𝑆𝑏𝑎𝑠𝑒1

10 kVA

𝑀𝑖∗

8s

𝑆𝑏𝑎𝑠𝑒2

5 kVA

𝐷𝑖∗

17 pu

𝐸0 = 𝑉𝑔𝑟𝑖𝑑

200 V

𝑘𝑝∗ 𝑖

20 pu

𝜔0 = 𝜔𝑔𝑟𝑖𝑑

376.99 rad/s

𝑘𝑞∗ 𝑖

5 pu

𝑃0∗ 𝑖

1 pu

𝑇𝑓𝑞 𝑖

7.96 × 10−3 s

𝑄0∗ 𝑖

0 pu The Basic VSG control

∗ 𝐾𝑝𝑞 𝑖

𝑇𝑖𝑞 𝑖

0.0025 pu

1.25 × 10−4 s

The Enhanced VSG control ∗ 𝐾𝑝𝑞 𝑖

𝑇𝑖𝑞 𝑖

0.0125 pu

- 72 -

1.25 × 10−4 s

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

TABLE 4.3

Fig. 4.12

Simulation Sequence

Time

Grid

∗ 𝑃0_1

∗ 𝑃0_2

Load

t < 21 s

Connected

1 pu

1 pu

Load1

21 s ≤ t < 24 s

Disconnected







24 s ≤ t < 27 s







Load1+2

27 s ≤ t < 30 s





0.6 pu



Simulation results of active power and frequency in the left column and reactive power and

voltage in the right column when both DGs are controlled by (a) the basic VSG control, (b) the basic VSG control + the proposed stator impedance adjuster, (c) the complete proposed enhanced VSG control.

posed enhanced VSG control scheme. A microgrid shown in Fig. 4.11 is studied. As it is shown in Fig. 4.11, impedances of output filters and distribution lines of each DG differ in per unit values. Other main parameters are listed in Table 4.2, and the sequence of simulation is shown in Table 4.3. Events of islanding from main grid, loading transition, and intentional active power sharing change are simulated at 21 s, 24 s, and 27 s, respectively. The simulation results are shown in Fig. 4.12. - 73 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

As it is illustrated in Fig. 4.12(a), when the microgrid is islanded at 21 s, and when load 2 is connected at 24 s, oscillation can be observed in active power when the basic VSG control is applied for both DGs. This oscillation is almost eliminated by applying the proposed stator impedance adjuster in Figs. 4.12(b) and 4.12(c). As the disturbance at 27 s is caused by change of active power set value of DG1, which is not a loading transition, active power oscillation cannot be eliminated in this case. However, the proposed stator impedance adjuster increases the damping ratio; therefore, the overshoots in Figs. 4.12(b) and 4.12(c) are smaller than that in Fig. 4.12(a). Meanwhile, the oscillation periods become longer, because the damped natural frequencies are decreased as it is discussed in Section 4.2.2. Note that the rate of change of frequency remains the same in all cases, which suggests that the proposed enhanced VSG control has no influence on the inertia support feature of VSG control. Moreover, in Figs. 4.12(a) and 4.12(b), reactive power is not shared properly in islanded mode, and is not controlled at set value in grid-connected mode, due to the voltage drop through the line impedance. Besides, reactive power control is not independent from active power control, as a change of set value of active power at 27 s also causes a change of reactive power sharing. These problems are all solved in the complete enhanced VSG control by applying the proposed bus voltage estimator, as shown in Fig. 4.12(c). It is also noteworthy that the steady-state deviations of DG voltage and bus voltage become smaller when the enhanced VSG control is applied. Fig. 4.13 illustrates the dynamic performance of reactive power and voltage during the loading transition at 24 s. Although the virtual internal emf 𝐸1 becomes much higher in the proposed enhanced VSG control owing to large voltage drop on the virtual stator inductance 𝐿𝑙𝑠 , the maximum voltage sag of PWM inverter reference 𝑉𝑝𝑤𝑚1 and output voltage 𝑉𝑜𝑢𝑡1 are kept within the same level as the basic VSG control. This implies that the voltage drop on 𝐿𝑙𝑠 is compensated well by the reactive power PI controller. Besides, although in the enhanced VSG control, the voltages become slightly oscillatory, the reactive power oscillations converge within 0.1 s.

Fig. 4.13

Zoom-in simulation results of reactive power and voltage of DG1 at 24 s.

(a) The basic VSG control; (b) the proposed enhanced VSG control.

- 74 -

Chapter 4 Parallel Operation of Multiple VSGs in Microgrids

4.6 Experimental Results Experiments are executed in an islanding microgrid, of which the circuit is the same as that of simulation shown in Fig. 4.11, except that instead of dc sources, ac supply rectified by diode bridge is used to imitate the dc output of DGs, and the breaker BK3 is opened, as shown in Fig. 4.14. The experiment setup is the same as those shown in Section 3.6. Experiment sequence is described in Table 4.4. Control Parameters are the same as those listed in Table 4.2, and the experimental results are shown in Fig. 4.15. Experimental results verify again the effectiveness of the proposed enhanced VSG control. First, by comparing Figs. 4.15(b) and 4.15(c) with Fig. 4.15(a), it can be observed that with the proposed stator impedance adjuster, the oscillation due to loading transition at 0.5 s is eliminated, and the oscillation due to change of set value of acitive power at 3.0 s is damped. It implies that the VSG control with the proposed stator impedance adjuster is able to track the loading transition rapidly and accurately without oscillation; meanwhile, the inertia support of the basic VSG control is kept. Even when an oscillation occurs, the overshoot is suppressed owing to increased system damping. Furthermore, by comparing Fig. 4.15(c) with Figs. 4.15(a) and 4.15(b), it can be concluded that by applying the proposed bus voltage estimator, the reactive power is shared according to the power rating ratio, and is immune to active power sharing change and line impedance mismatch in per unit values. Although ripples in RMS value of output voltage can be observed due to a slight load unbalance, the reactive power is controlled well when the enhanced VSG control is applied.

Fig. 4.14

Experiment circuit.

Table 4.4

Experiment Sequence

Time

∗ 𝑃0_1

∗ 𝑃0_2

Load

t < 0.5 s

1 pu

1 pu

Load1

0.5 s ≤ t < 3 s





Load1+2

3s≤t